The Republican-controlled Senate Budget Committee defied President Reagan yesterday and approved a bipartisan budget for next year that slashes $25 billion from his defense request, raises taxes by $18.7 billion and ignores many of his domestic cutback proposals.

The budget, which meets the $144 billion fiscal 1987 deficit target of the new Gramm-Rudman-Hollings budget-control law, was approved 13 to 9 with support from a majority of Republicans as well as Democrats on the panel.

But it achieves the goal in a manner that conflicts sharply with priorities of Reagan's budget for next year, and it was quickly denounced by Office of Management and Budget Director James C. Miller III.

The proposed tax-and-spending blueprint for fiscal 1987 will go to the Senate floor early next week. Senate Majority Leader Robert J. Dole (R-Kan.) expressed reservations about the size of defense spending cutbacks and tax increases, but committee Chairman Pete V. Domenici (R-N.M.) predicted that it "or something very close to it" will be approved.

House Democrats are working privately on a budget plan of their own but are reportedly having trouble meeting the deficit target without resorting to tax increases, even though they are considering far deeper defense spending cuts than the Senate panel proposes.

The Senate panel's budget is unprecedented in that it was put together from the start by Domenici working jointly with Sen. Lawton Chiles (D-Fla.), ranking Democrat on the panel. Previously, Senate Republicans attempted to reach an agreement first with Reagan. But unhappy with budget dealings with the White House last year and frustrated by signs that the White House wanted to wait until later to negotiate this year, they turned to the Democrats.

"At this point, it seems to me they [White House officials] almost acted as though they didn't care," Domenici said.

But Miller was sharp in his criticism of the committee's work. He said its domestic spending cutbacks are "timid and minimal" and contended the tax increases and defense cutbacks are "too much." He made no appeal for negotiations.

Later, presidential spokesman Larry Speakes also denounced the budget proposal, saying that it reaches a "desirable goal by totally unacceptable methods."

The committee's budget allocates $295 billion for defense, which committee members said should be enough to meet the costs of inflation, even though it is $4 billion less than Domenici's earlier estimate of what it would take to cover inflation. Reagan had asked for $320 billion, enough to provide an 8 percent increase after accounting for inflation.

Domenici and Chiles contended that the allocation would be sufficient to sustain current program levels through next year, with anticipated growth of 1 percent beyond inflation for the two following years. But even some senators who voted for the plan in committee complained that the amount was too small and indicated that they may support an increase on the floor.

"We really haven't taken care of the inflationary costs. I think it's a little severe," said Sen. Ernest F. Hollings (D-S.C.).

In supporting $18.7 billion in tax or other revenue increases for next year (about $75 billion over three years), the committee embraced $5.9 billion in revenue increases that Reagan had proposed ($21.6 billion over three years) but did not spell out where the rest of the money should be found.

In comments to reporters, Domenici suggested the possibility of excise tax increases, loophole closing, a minimum corporate tax and a tax-amnesty program, under which delinquent taxpayers would be encouraged to pay back taxes. The committee made clear it was not calling for an increase in individual income taxes.

Reagan has adamantly opposed tax increases beyond the relatively minor revenue measures in his budget, and several committee members indicated that they voted against the package because of its tax increases. But Domenici contended that the committee could not have achieved the $144 billion deficit target without new revenues.

In approving $14.6 billion in non-defense spending cuts, the committee came up with about half the domestic savings that Reagan wanted and rejected most of his proposals for program terminations.

It proposes to end the Work Incentive (WIN) program but seeks only cutbacks for many others, such as Urban Development Action Grants, the Economic Development Administration and the community development block grant.

It provided for 3 percent annual pay increases for federal workers, both civilian and military, over the next three years, along with full cost of living adjustments for government pensions as well as Social Security.

While most programs were frozen or cut, the committee allowed for increases in embassy security, the space program (including a new shuttle), the Superfund toxic-waste cleanup program, air travel safety, farm credit protections and a variety of health, education and law enforcement programs.

Even though Congress agreed last year to end general revenue-sharing with local governments this year, the committee allowed room for continuation of the program for another half-year if offsetting revenues are approved to finance it. A move to continue to the program for a year was rejected, however.

Efforts to increase domestic spending in several areas, including education and health, failed.

Voting for the Domenici-Chiles budget were Republicans Domenici, Nancy L. Kassebaum (Kan.), Rudy Boschwitz (Minn.), Mark Andrews (N.D.), Charles E. Grassley (Iowa), Slade Gorton (Wash.) and John C. Danforth (Mo.) as well as Democrats Chiles, Hollings, J. Bennett Johnston (La.), Howard M. Metzenbaum (Ohio), Donald W. Riegle Jr. (Mich.) and J. James Exon (Neb.). Voting against it were Republicans William L. Armstrong (Colo.), Steven D. Symms (Idaho), Robert W. Kasten Jr. (Wis.), Dan Quayle (Ind.), Orrin G. Hatch (Utah) and Democrats Hart, Jim Sasser (Tenn.), Daniel Patrick Moynihan (N.Y.) and Frank R. Lautenberg (N.J.).