The Senate Finance Committee agreed yesterday to reduce the tax bite on Alaskan oil under President Carter's proposed windfall profits tax, further diluting the measure from the version passed by the House.

By a 12-to-0 vote, the panel decided to scrap a stiffer tax on Alaskan oil that the House had approved and instead include petroleum from the North Slope in a geenral "upper tier" category comprising oil produced after 1972.

At the same time, the panel voted to endorse a House-passed proposal that would tax all "upper tier" oil at a 60-percent rate rather than at the 50-percent levy Carter originally had sought. That vote was 11 to 7.

The combination of actions trimmed another $5 billion from the total new revenues the Finance Committee's tax would raise over the next 10 years, leaving it at $65 billion, or less than two-thirds of what the House would collect.

With yesterday's decisions included, the Finance Committee's bill would tax away 27 percent of the so-called "windfall" the oil industry is expected to reap from decontrol of oil prices -- compared to 43 percent for the House measure.

Nevertheless, yesterday's votes constituted a victory of sorts for the administration, which managed in the process to head off more generous concessions for Alaskan oil.

The panel earlier rejected a bid by Sen. Mike Gravel (D-Alaska) to exempt Alaskan oil entirely from the windfall tax -- a move that would have trimmed the 10-year total for new revenues by as much as $12.2 billion.

And the panel's endorsement of the 60 percent tax rate for "upper tier" oil marked a stiffening of the president's original proposal. Carter has asked for a 50 percent rate for this category, but later backed the House bill.

The committee also voted down a proposal by senators from oil-consuming states that would have boosted the tax rate on "upper tier" oil to 70 percent. Sponsors wanted the extra tax revenues to finance energy tax credits.

The committee is expected to work on miscellaneous provisions in the bill this morning and then begin work tomorrow on a staff recommendation on which tax credits to tack on for home-owners and businesses.

The panel earlier approved about $99 billion in tax credits, but agreed to cut then back after it became clear that the tax breaks would exceed the amount of new revenues that the windfall measure would bring in.

The tax credits are being opposed by the administration, which wants to use the revenues from the windfall tax to finance a proposed synthetic fuels development program and additional mass transit grants.