The House, by a 217 to 196 margin, yesterday voted to cut off further funding for the controversial Clinch River Breeder Reactor in Oak Ridge, Tenn.

The vote against the advanced nuclear power plant, which is designed to "breed" more plutonium than it uses, marks the latest twist in the saga of the project, which was originally authorized by Congress 12 years ago. The House action was on an amendment by Rep. Lawrence Coughlin (R-Pa.) to delete funding for the project from a stop-gap appropriations bill.

"The defeat of Clinch River is a real victory for the American taxpayer," said James D. Davidson, chairman of the National Taxpayers Union, which is one of the groups that has been fighting the project.

But in fact, yesterday's vote is far from the final word.

Senate Republican Leader Howard Baker of Tennessee, a staunch supporter of the project located in his home state, is expected to try to restore funding for Clinch River to the bill when the Senate takes it up later this week.

An effort in the Senate to strike funding for Clinch River failed on a 49 to 48 vote in September.

Even if the Senate goes along with the House and President Reagan, who has been a major advocate of Clinch River, signs the bill, that does not mean that work on the project will come to a halt.

Gordon Chipman, deputy assistant secretary of Energy in charge of the breeder reactor program, said yesterday enough fiscal 1982 money remains on hand to keep work on Clinch River moving ahead until the new Congress convenes in January.

"This vote does not deauthorize the project," Chipman said, "and the law requires that until Congress deauthorizes the project, all monies appropriated must be spent toward its original objective. So in a practical tical sense, the project will continue until such time as it runs out of prior year money or it is deauthorized," he said.

Chipman said construction at the site, which was finally begun in September after a five-year delay that resulted from President Carter's decision in 1977 to halt the project, was "moving ahead aggressively."

Congressional opponents of Clinch River have come closer to cutting off funding with each vote. Critics have gained ammunition from a new General Accounting Office estimate of $8.5 million for the total cost of the program.

This sum is more than double the current Energy Department estimate of $3.6 billion. But GAO included $3.9 billion in interest. Interest is usually not factored into the cost of research and development projects.