Limited sanctions against South Africa applied by several countries have already made a serious impact on the nation's economy, slashing exports of coal, the second biggest source of income after gold, and jeopardizing the jobs of as many as 40,000 miners.

An association of mining companies called the Chamber of Mines warned this week that if the European Parliament yielded to appeals for total sanctions, Far Eastern countries might also stop buying South African coal, collapsing the country's exports altogether. Fearful of that prospect, some mining companies are making contingency plans for massive job cutbacks in the industry.

The disclosure has brought the issue of sanctions sharply into focus here. It has shown white South Africans, many of whom believed the country's highly developed economy could easily withstand whatever sanctions might be introduced, that their prosperous industries may be more vulnerable than they realized.

But despite these shocks to one of the country's most important industries, there is no sign that it is making any political impact on the country's rulers. The administration has offered no statement of concern.

Members of the predominantly English business community are dismayed, but analysts here believe that the national economy would have to be brought close to collapse before the Afrikaner-dominated government would make political concessions to end sanctions.

Industry sources report that embargoes on South African coal imposed this year by Denmark and France and a growing reluctance by other countries to buy coal from here have cut projected exports for 1986 by 7.5 million metric tons, or 17 percent.

South Africa has also been forced to sell its coal at about 10 percent below the world price of $25 to $26 a metric ton for the low to medium grades it produces, in a bid to avoid losing more exports.

If that happened, the chamber said, up to 40,000 of the country's 110,000 coal miners might lose their jobs. It said some mining companies were already making contingency plans for retrenchments.

Coal is second only to gold -- of which South Africa mines half the world's total production -- as a revenue earner here. Coal exports last year earned $1.5 billion.

It was also the bluest chip among growth industries here. Production soared from 57 million tons in 1971 to 173 million tons last year, a special coal port has been built on the Indian Ocean coast at Richard's Bay, and projections were that coal would overtake the diminishing deposits of gold as the country's major export by the end of the century.

Now, partial sanctions by just two countries, one of them tiny, have thrown this key industry into what one company official described today as "a slough of despond."

The threat of retrenchments has also highlighted the conflict between white management and black unions over the issue of sanctions. The chamber's statement has sparked a heated row between the mining companies and the National Union of Mineworkers, which is the biggest of the newly established black labor unions here.

Most of the unions support the call by black political leaders for international sanctions to end apartheid. The mineworkers' secretary, Cyril Ramaphosa, strongly endorsed this call in a recent speech to British coal miners in Wales.

In its statement Monday the chamber said it found Ramaphosa's support for sanctions "inexplicable," since if the retrenchments had to be made it would be mostly members of his union who would suffer.

An angry Ramaphosa responded by accusing the chamber of making an "irresponsible" threat of retrenchments to try to counter the sanctions campaign. He warned of "massive industrial action" if retrenchments took place.

"The chamber should be looking instead at the reasons why many people are calling for sanctions, including the payment of starvation wages to miners," Ramaphosa said.

Allen Cook, chairman of the chamber's colliery committee which drafted the report, admitted in an interview today that the statement was issued "as a warning to the sanctions lobby."

He said it had been made on the eve of President Reagan's policy speech on South Africa Tuesday to impress on the president what serious repercussions sanctions would have for the country's blacks.

Although the United States imported only 800,000 tons of South African coal a year, "we were afraid that if America announced a boycott this could have a domino effect on other countries," Cook said.

Then, he said, Europe, which collectively buys 24 million tons a year, and Japan, which buys more than 7 million tons, might follow.

British Foreign Secretary Geoffrey Howe spent the second day of a European Community-mandated peace mission here meeting black and white businessmen and members of the white liberal opposition.

Everyone Howe has met so far on his one-week mission has been a strong opponent of sanctions. The country's major black leaders, most of whom favor sanctions, are refusing to see him because they say his mission is a maneuver by Britain to evade presure from its European partners to apply collective sanctions.

Howe left this afternoon for Lusaka, where he was due to have talks with Zambian President Kenneth Kaunda. He will return to South Africa tomorrow via Botswana, where he is scheduled to meet President Quett Masire. He is also due to visit the small neighboring black states of Lesotho and Swaziland, whose dependence on South Africa means they could suffer badly if sanctions are applied.

Meanwhile, three more blacks were officially reported killed in unrest incidents during the past 24 hours.

The Bureau for Information, which is the only authorized source of news about the unrest under the state of emergency, said two men were shot dead by police during a clash in a black township near Port Elizabeth, and an unidentified woman was burned to death in the tribal "homeland" of KwaNdebele, north of Pretoria.