The Republican chairman of the Senate Budget Committee yesterday proposed a big cut in President Reagan's military spending plans for next year as the Democratic-controlled House staged what amounted to a public execution of the president's budget proposal.

The House voted, 312 to 12, against the president's budget, with most Republicans voting against it, most to protest a partisan "flim-flam" by the Democrats to embarrass Reagan.

While House rejection of the president's budget was expected, the defense spending cutback proposed by Senate Budget Committee Chairman Pete V. Domenici (R-N.M.) posed a more serious problem for the administration.

Maneuvering to break a stalemate with Democrats over defense spending, Domenici unveiled a budget plan of his own for next year that would allow no growth beyond inflation for the military.

Domenici's $299 billion spending proposal for defense came as a surprise because he had been holding out for an increase that would exceed inflation. A decision by the Senate's GOP budget chief to settle for a hold-the-line military budget for next year -- with annual increases of only 1 percent over the following two years -- indicated the administration will have to scramble to avoid a reversal of its military buildup.

Reagan had proposed an increase of 8 percent in his $320 billion military request next year. Reagan's request totaled about $21 billion more than Domenici proposed and $30 billion more than Democrats appeared willing to support.

Domenici's plan also called for an increase of $70.3 billion in taxes over the next three years, starting with $16.2 billion in fiscal 1987. His plan for next year would include $6 billion in revenue increases proposed by Reagan, along with $10 billion in unspecified increases that are expected to include revenues from an amnesty plan for delinquent taxpayers.

While embracing some of the president's domestic spending cutbacks, Domenici rejected others, including most of Reagan's "privatization" plans to sell off federal assets. He would freeze or cut most programs, terminate some but not as many as the president proposed and add funding for programs such as law enforcement, air traffic safety and a space shuttle replacement.

"I think it goes without saying that a lot of people at the White House won't like it," said Domenici, while predicting that something close to it will eventually be approved by the committee on a bipartisan basis.

Sen. Lawton Chiles (D-Fla.), ranking committee Democrat, said he was "a little discombobulated" by Domenici's proposal in light of their earlier attempts to negotiate a bipartisan compromise, which apparently fell apart late Wednesday in a "misunderstanding," as Domenici put it, over defense spending.

"It throws everything up in the air, and it will take a while to settle," Chiles said. Domenici, however, said he expected to get a committee agreement in time for action by the full Senate before the Easter recess March 27.

The Senate committee's attempts at bipartisanship, however halting, contrasted sharply with the partisan free-for-all on the House floor as Democrats and Republicans wrangled all afternoon over whether it was proper to be voting on the president's budget.

Democrats, mindful of politically painful spending cuts that Reagan proposed and eager to force Republicans to vote on them, contended that the House owed both Reagan and the country a vote on the president's plan. Republicans cried foul, complaining that the Democrats were playing politics and engaging in "president-bashing."

"This is all a farce today, a sham," House Minority Leader Robert H. Michel (R-Ill.) charged, contending that Reagan's budget was "unrealistic" only because of budget-balancing constraints imposed by Congress. "A Barnum and Bailey show, a carnival," said Rep. Bill Frenzel (R-Minn.). "A charade to cover up their own lack of progress" in producing an alternative, said Rep. Lynn M. Martin (R-Ill.), acting ranking Republican on the House Budget Committee.

"Americans deserve to know whether their elected representatives stand on the president's budget," responded Budget Committee Chairman William H. Gray III (D-Pa.).

"I haven't heard any comments about the merits of the president's budget . . . . Now isn't that curious?" observed House Majority Leader James C. Wright Jr. (D-Tex.).

In the vote on Reagan's budget, Democrats cast no votes for it and 238 votes against it; one Democrat voted present. Among Republicans there were 12 votes for the budget, 74 against it and 77 present.

Meanwhile, Senate Republican leaders reached agreement with the administration on details of a deficit-cutting plan left over from last year, including a heavily contested plan for sharing offshore oil and gas receipts with state governments.

But the House earlier passed a different version that the White House has said Reagan would veto, and it quit for the weekend before the Senate took up the measure last night. This means the issue cannot be resolved before next week. House-Senate agreement on the measure by tonight was critical because it contained a permanent extension of the 16-cents-a-pack tax on cigarettes. A temporary extension expires Saturday, after which the levy drops to 8 cents a pack.