This is where copper is coming a cropper.

The great open pit copper mines of Arizona, New Mexico and Utah, world-dominant for most of this century, are mired in a three-year depression.

It has halved mining employment, idled 16 of the nation's 28 largest mines, triggered the longest strike in industry history (21 months and counting here at Phelps Dodge's mile-wide Morenci mine), generated net industry operating losses of nearly $3 billion since 1981 despite a 29 percent reduction in per-ton production costs and set off a round of almost panic-stricken divestitures by the same oil companies that went on a cash-happy shopping spree for copper mines in the 1970s.

This week, Phelps Dodge announced that its smelter in Ajo will close April 4, laying off 200 workers. Prognoses for the survival of the industry as a whole -- from whose vivid, sometimes violent, history could be chronicled the taming of the American Southwest -- range from dire to dour.

Copper is not the only afflicted metal in this country.

Lead producers have been stung by the unleading of gasoline; the great iron ore mines of Minnesota's Mesabi Range have been losing a generation-long battle with low-cost imports; gold and silver prices have gone soft, and aluminum producers have been hurt by the high cost of power, which they use abundantly in smelting.

Nationwide, metals mining employment dropped from 109,000 in 1981 to 44,800 last year.

But the $2.4 billion copper industry is the largest metal miner and, at the moment, the most crippled. And it is mined in a sparsely populated, politically vulnerable part of the country, reducing prospects for a congressional bailout.

Copper's humiliation has come at the hands of a rogue's gallery of economic and social forces that mugged a swath of Smokestack America throughout the 1980s.

This lineup includes: low-wage Third World competitors that have been overproducing (and driving the world copper price to Depression-era depths) to raise the money their countries need to pay off international loans financed, in part, by U.S. taxpayers; federal clean air standards that have forced the industry to spend -- and often misspend -- hundreds of millions of dollars on antipollution processes that have added to cost but not productivity, and a strong dollar that has devoured export markets as voraciously as it has sucked in copper imports.

Besides these generic causes of U.S. deindustrialization, there is a another problem specific to copper.

Most of the known high-grade copper ore in this country has been mined. The grade or copper content of the ore in the gargantuan Chuquicamata mine in Chile, which has become the Saudi Arabia of copper, is twice that of a typical U.S. mine, and the ore grades in Zaire's nationalized mines are more than five times the U.S. average.

Given these multiple ills, the copper debate will bump into some hard questions. Are old-line "dirty" industries like copper worth saving? If so, are they capable of salvation? Or, sooner or later are they bound to be done in by broad forces of economic change?

In the darkest hours of auto and steel, such questions were not entertained seriously. At stake were too many jobs, too much national security, too expansive an economic ripple.

"The next 12 to 18 months will decide whether there's going to be a domestic copper industry," said Bruce Wright, administrative aide to Rep. Morris K. Udall (D-Ariz.), who earlier this month introduced a rescue bill in Congress.

"The only difference between us and the industries that get bailed out," said Carl J. Forstram, plant manager of the Phelps Dodge mine here, "is that we don't have the votes in Congress."

Udall's bill, introduced on behalf of the new congressional Copper Caucus, would provide a five-year "recovery window" by negotiating production limits for foreign competitors. (Under the legislation, competitors that refused to live within the limits would have tariffs slapped on their exports to the United States). Import Quotas Urged

Prospects for passage are not good. There are23,000 jobs left in copper mining and smelting, a fraction of the auto and steel payroll. Moreover, the copper fabricating industry -- which buys refined copper from U.S. and overseas producers -- employs five times as many workers as the mines.

Last year, after the International Trade Commission found that unfair foreign competition had hurt the American copper producers, the fabricators opposed ITC recommendations for tariffs or quotas, fearing that either approach would create a two-tier pricing structure -- one U.S. price and a lower world price -- that would place them at a competitive disadvantage.

The Reagan administration sided with the fabricators. "It was a political year, and in a political year, you count heads," said Robert Wardell, president of the Copper and Brass Fabricators Council. "We had 125,000 jobs, the producers 25,000."

"It's not just the politics of it," said Don Phillips of the Office of the U.S. Trade Representative, which turned down the ITC request. "If, by imposing tariffs, you are going to lose more jobs in fabrication than you save in mining, that's a legitimate economic consideration."

If the jobs argument alone cannot carry the day for the mines, Udall and others say defense considerations should.

Copper is used in everything from ammunition casing to battlefield communications lines to engine parts. The nation experienced copper shortages during each of its last three wars; the shortages were deemed so serious that in the late 1960s the federal government, through the Defense Production Act, helped finance the development of several large private mines.

Copper is one of 61 commodities designated by Congress as part of the National Defense Stockpile, but as of 1984, the government had filled only 3 percent of its target stockpile of 1 million short tons of copper. The industry has been clamoring for additional reserve purchases in this, its hour of need, but government experts say that, given the current world oversupply of copper, there are more pressing purchasing priorities.

"The national security danger is that this is an industry that can't be turned on and off like a faucet," said C.J. Hansen, president of the Arizona Mining Association. "Once you close mines, you tend to lose them."

Industry leaders believe that is what Chile is banking on. They say that Chilean overproduction -- which they describe as a deliberate strategy of selling two pounds of copper at 50 cent a pound rather than one pound at $1 -- amounts to a predatory "squeeze play" designed to drive high-cost U.S. producers under.

Chile can make a profit on low-price copper; the U.S producers, whose costs are 50 percent higher, cannot. Already the U.S. share of the world market has dropped from 50 to 13 percent over the past two generations.

Domestic copper producers are enraged that the Chilean copper industry has been aided by loans from the International Monetary Fund and World Bank granted in what J. Hugh Leidke, chairman of the Pennzoil Co. (which recently put its copper subsidiary, Duval Corp., up for sale), calls a "global Ponzi game" to ensure that developing countries will have the revenue to pay off earlier loans.

Most parties to the copper debate agree that the domestic industry has legitimate gripes. But one school holds that, even so, any rescue effort would only postpone the inevitable.

"Let's face it, what's happening with copper is what we are supposed to want to happen," said Robert Horton, director of the Interior Department's Bureau of Mines. "The developing countries are in fact developing. No government can stand in the way of long-term trends for very long."

Even Arizona Gov. Bruce E. Babbitt has been muted in his calls for federal help. "The governor realizes that copper's heyday has come and gone," said Jim West, Babbitt's press secretary. " . . . He doesn't want to raise hopes that will only be dashed later. He's more interested in economic diversification." Union Move Blunted

Behind the cold-eyed assessment of economic history, there is a human and intensely poignant side to the decline of a "company-town" industry.

Copper is the source of the genteel wealth of the Hearsts and the Guggenheims, but its history is that of a rugged, Wild West industry, pioneered by prospectors who spilled as much blood fending off each other as they did fighting the Apache.

Because copper deposits were so remote, mining companies built company towns to attract and hold a stable work force. Labor relations in such towns have ranged from violent to imperial to benign; one historian has likened them to imperial Britain's mercantilistic outposts, with their rigid social and economic strata.

Seventy years ago, the Industrial Workers of the World ("wobblies") tried to establish a foothold in the copper towns. But in 1917, in one of the infamous episodes of U.S. labor history, 1,250 workers and IWW sympathizers at Phelps Dodge's Bisbee, Ariz., mine were rounded up by a sheriff's posse on orders from Phelps Dodge officials and sent by train to a town in New Mexico with a warning never to return.

The labor movement in the copper mines never has been the same, nor has management ever been quite so heavy-handed. Company towns like the one here grew into little mountaintop oases of the good life: palm trees, manicured lawns, good schools, plenty of hunting and fishing, all set in the stark beauty of the southern Rockies.

By 1983, when the current Phelps Dodge strike began, workers here were getting wage and benefit packages worth an average of $36,000 a year. "As an industry, we had gotten fat, dumb and happy," Hansen said.

Most of the Phelps Dodge workers grew up as second- or third-generation miners; the whole town had the quality of a extended -- and fairly happy -- family. Race relations among Hispanics, Anglos and Indians were good, on the whole.

"It was a pretty good life, no question," said Angel Rodriguez, head of United Steel Workers Local 616, the largest of 13 unions that used to represent 2,000 workers here. A Brutal, Bitter Strike

It came unglued July 1, 1983. Other copper companies had agreed that spring to a pattern contract that involved a wage freeze; Phelps Dodge also wanted to eliminate cost-of-living adjustments and extract some other concessions. When the unions went on strike, the company decided to keep the mine open, which it was able to in the critical first days only with the help of National Guard units mobilized by Babbitt.

It has been a brutal, bitter strike. There have been no deaths, but vandalism in Morenci is in the $250,000 range, company officials say; comparable damage has been done in Ajo, Douglas and other Phelps Dodge towns.

Brother has been set against brother, friend against friend, father against son as miners have made the agonizing choice between working and striking. About half the jobs at the mine are filled by ex-union members who crossed their own picket lines.

The strike has been a disaster for the unions. Phelps Dodge has been able to operate; it says that it even set production records last fall. New workers' wage scales have been cut by one-third, and all 13 unions were kicked out last fall in a decertification vote that is still being appealed. Workers at other mines in Arizona, fearful for their jobs, are decertifying their unions as well.

Nearly 21 months after the strike began, strikers and "scabs" still wave ritual obscene gestures at one another each afternoon at the shift change, but the strike long since has been lost.

"I'm just sort of hanging around to see how the [appeal] of the decertification vote comes out," said Janner Nessler, a striking filter helper. Most of his fellow strikers long ago drifted away to Tucson or Phoenix or Stafford, leaving behind not just their jobs, but also their roots, their homes, their relations.

Even with the cost-cutting and union-busting, the Phelps Dodge mine here may not be able to make it. In January the company had to close its Morenci smelter into which it had poured $90 million in an effort, utimately futile, to comply with an Environmental Protection Agency consent decree.

"In hindsight, they would have been better tearing the smelter down and starting from scratch," Hansen said. "They tried for an innovative approach to pollution control, and they could never get it to work."

Phelps Dodge is not the only company to miscalculate antipollution strategy. The Duval Corp. spent millions developing a state-of-the-art hydrometallurgical smelting system that does not foul the air but has proven too costly to operate.

When the Phelps Dodge smelter here closed, it meant laying off permanently 600 workers, some of whom were the very ex-union members who had estranged themselves from their families by choosing to work. Officials said the Ajo smelter, the town's only industry, could reopen if copper prices rise. Japanese Firms Buy In

Phelps Dodge, Arizona's largest copper producer and the nation's second largest (behind Kennecott), lost $267.8 million in 1984. The most optimistic reading of its future is uncertain. And if a miracle rescue comes, it may come from a strange corner of the globe.

Earlier this year the Sumitomo Corp., a Japanese trading company, signed a letter of intent to purchase 25 to 40 percent of the Morenci mine. Sumitomo is following the footsteps of the Mitsubishi Corp., which in 1980 became a one-third owner of Kennecott's Chino Mines in New Mexico.

Japan is a copper importer, and its modern, post-World War II smelters, which are low in pollution, are always hungry for more ore concentrate. The company apparently plans to ship the concentrate -- which is 25 percent copper -- across the ocean from Morenci and smelt it in Japan.

If that happens, the mine here would serve a function commonly associated with those in the Third World as a supplier of a raw metal to an industrial power that would smelt it, fabricate it and sell it on the world market.

A circle, of sorts, would be closed in Morenci. The world's first and foremost industrial giant, unable to compete with the developing nations, would become one.

"The Japanese are our best hope," said J.D. Ferrin, an instrument repairer who moved here with his wife and three children a few months after the strike began because the pay was 50 percent better than he could make anywhere else.

"I can't imagine them sinking a lot of money in here and not giving it a good try," he said.