The Senate Finance Committee voted yesterday to exempt newly discovered oil from President Carter's proposed windfall profits tax -- the first in a series of expected actions designed to lessen the legislation's bite.

The vote would trim $14 billion from the estimated $104.3 billion that the House-passed measure would collect between now and 1990. Carter wants to use this money mainly to finance his synthetic fuels program.

But with yesterday's action included, the committee has stripped $19.5 billion from potential revenues in the windfall tax bill, and approved $63.2 billion in new energy-related tax credits -- in effect "using up" $82.2 billion.

At the same time, committee members served notice they are considering additional exemptions that could take another $61.9 billion from the expected revenues over the 10-year period. The committee may reconsider the tax credits later.

Meanwhile, two senior Finance members, Sens. Harry F. Byrd Jr. (Ind.-Va.) and Bob Dole (R-Kan.), announced they would seek to add to the windfall bill a controversial amendment to repeal a key provision of the 1976 Tax Reform Act.

The provision, known as "carryover basis," was designed to increase capital gains taxes on profits from sale of inherited property. Heirs who sell such assets now often pay relatively little tax.

President Carter has threatened to veto any bill that seeks to repeal the provision, but attaching it to the windfall profits tax would make such action difficult. Repeal would cost the Treasury $800 million a year.

Yesterday's action by the Finance Committee was the first major vote it has taken on the portion of the bill that would tax crude oil. Until now, the panel has been drafting energy tax credits.

Chairman Russell B. Long (D-La.) has promised Carter that Congress will have a windfall profits bill on his desk by the end of October. However, most observers now expect that tax to be a weak one.

The tax action came as, separately, the Senate Energy Committee continued work on Carter's proposed synthetic fuels development program inching through procedural questions in the early stages of the drafting process.

Although Carter has proposed financing the synthetic fuels program with revenues from the windfall profits tax, Energy Chairman Henry M. Jackson (D-Wash.) has insisted that the fuels plan "stand on its own" without such linkage.

The two committees have been competing quietly for control over the energy program, but observers think Long may have a jump because of his panel's claim on windfall tax revenues.

Yesterday's action in Finance came despite vigorous opposition from Carter administration representatives, who argued that exempting new oil would cut deeply into expected revenues without encouraging much more production.

The panel had been expected to make some changes anyway because critics had argued that the House provision was written to discourage new production until 1990, when the tax on newly discovered oil was to be lifted.

However, the panel went still further and exempted newly discovered oil entirely. The changes, adopted on a vote of 13 to 0, also would liberalize the definition of newly discovered oil to include any not in production last year.

Yesterday's action drew one public expression of doubt. Sen. John C. Danforth (R-Mo.) mused that the panel had better compare its votes on the tax and the credits or "we will end up with a tax of zero and expenditures of $200 billion."

The committee also is expected to pare back the tax bite on other categories of oil, exempting Alaskan oil, petroleum from stripper wells, tertiary oil and oil pumped by small "independent" producers.

So far, the Finance panel has approved tax credits for unconventional fuels, solar power, home insulation, furnaces, heat pumps, wood stoves and hydroelectric generating equipment. Long has told reporters he hopes to finish work this week.