Today the cheering stopped. The people of Times Beach, who learned yesterday that the Reagan administration will spend $33 million to move them away from their contaminated community, are confronting the problems money can't solve.

They face the death of their town and a future among strangers.

Now, too, they must contemplate the reason for this federal rescue mission: the finding that their streets are laced with dangerous levels of dioxin, one of the most toxic compounds known.

"Ours is a very small town where kids could play in the streets and mothers never had to worry," said Evelyn Zufall, who lived here for 29 years, drove a school bus and raised seven children. "It's very sad, almost like someone died and you're visiting their grave. This was a nice place once, and now we have to bury it."

This, the people of Times Beach say, is the real story of the nation's hazardous waste nightmare, a story much bigger than paper shredders and contempt citations and the suggestion of political scandal that has captivated Washington.

"It's not just that you lose your house. You can replace your house," said Times Beach truck driver Howard Coffman, who abandoned his concrete home here two months ago, when the government first documented the dioxin contamination.

"But we've lost our peace of mind. We're losing all our friends. On Sunday, we went to see a neighbor, and it took us 45 minutes. I knew just about everyone on 'the Beach.' And to tell you where they are now, there's no way.

"I'll be grateful for that money, but money don't make up for what we lost. You can't put dollars and cents on friends."

The sentiments were echoed by dozens of Times Beach people who, moments earlier, had cheered their imminent deliverance from dioxin. About 300 of them gathered at a hotel near here yesterday to hear Environmental Protection Agency Administrator Anne M. Burford announce the buy-out of their one-square-mile town.

It will be the largest government purchase of contaminated property in U.S. history, more than double the scope of the relocation project at New York's Love Canal.

"I wish the whole country could see our faces," Zufall said as she waited expectantly with friends for Burford's announcement. "We'll always wonder if our health problems were caused by that poison, or if we would have had them anyway."

Residents of Times Beach pressed against a glass door, straining for a look at Burford as she delivered the announcement in a locked conference room at the hotel. Her words reached the people by loudspeaker as six police officers restrained the crowd, keeping the Times Beach residents away from Burford "to prevent incidents," according to one policeman.

Six boys in polo shirts and girls in pigtails pushed to the front, holding a hand-lettered poster against the glass for Burford to see. In the center was a drawing of a skull and crossbones, emblazoned with the words "Times Beach, Doomed Without Help!"

Times Beach is only one of at least 100 sites in Missouri that are believed contaminated by dioxin, and scientists have just begun to document the full scope of the problem. The compound, a byproduct of antiseptics manufactured at a Missouri chemical plant, was mixed with oils and sprayed on dirt roads across the state in the early 1970s to suppress dust.

Government officials now know that dioxin in tiny doses causes cancer and other diseases in laboratory animals, but its effect on humans remains a subject of debate.

Residents say they will never forgive the state agencies or the EPA officials who had indications of the problem as early as 1973, but did not move aggressively against it until last year.

Even now, residents said, they believe they wouldn't have received federal aid had they not become a media sensation and a focus of the controversy enveloping the EPA hundreds of miles away in Washington.

Burford, her voice cracking, looked at the people through the glass windows of the conference room yesterday and assured them that this was not so. The decision came about, she said, because she and her staff "have been deeply concerned about you," and because President Reagan "cares about you deeply." CAPTION: Picture 1, Times Beach residents watch from door of hotel where EPA administrator Anne M. Burford announced the federal buy-out plan. UPI; Picture 2, Residents' children hold sign as Burford details the $ 33 million prgram. AP