The Legal Services Corp. survived another attempt on its life yesterday as the Senate beat back efforts to eliminate or trim sharply its funds for legal aid to the poor.

However, the embattled organization was wrapped in new restrictions critics designed to prevent it from engaging in politics, lobbying and filing broad-based suits on behalf of a class of citizens. The result of Senate voting was to assure the corporation's continuation -- barring a presidential veto -- with a 1982 budget reduced 25 percent from last year and a narrower scope of legal activity on behalf of poor people.

The corporation, which grew out of the 1960s' social ferment, has been in trouble all year. Opponents charge it has strayed into social activism and political lobbying from its initial task of defending the poor.

President Reagan wants the program abandoned; he proposed no money for it. The Senate yesterday approved an appropriation of $241 million, compared with the $321 million spent in 1981.

The money is part of an $8.6 billion appropriation for the departments of Commerce, Justice and State, a spending level a half-billion dollars higher than the ceiling Reagan has requested. The Senate stopped short of final passage.

A motion to cut Legal Services' financing further to $100 million was tabled after an attempt by Sen. Jeremiah Denton (R-Ala.) to eliminate its appropriation failed, 61 to 21.

Denton charged that the corporation's local lawyers had inappropriately campaigned for such social changes as a graduated income tax in Massachusetts, food-stamp increases and the return of land in Maine to Indian tribes.

Several critics contended the job of guaranteeing legal representation for the poor should be left to bar associations and private lawyers.

"This corporation has become a weapon of social activists in their unceasing battle with the government," said Sen. Strom Thurmond (R-S.C.).

Supporters answered that private attorneys could not replace the program's lawyers and said any further cuts in its financing would effectively eliminate the concept of equal legal representation for poor citizens.

But the supporters accepted restrictions. These would prohibit the corporation's lawyers from representing illegal aliens, bar lobbying and political activity, and require that 60 percent of a local legal agency's directors be lawyers from within the state.

They also would prevent the corporation from financing class-action suits, which seek to advance the rights of a large number of citizens.

The House passed a similar bill last summer with even stricter restraints, including one barring corporation assistance in cases of homosexuality.