The Senate Finance Committee moved to restore unemployment benefits to ex-servicemen yesterday as it finished work on domestic spending cuts to help reduce the deficit and prepared to start voting today on ways to raise $20.9 billion in new revenues next year.

The committee, under instructions to cut spending within its jurisdiction and to raise taxes, tidied up a few final provisions on the cuts it voted last week. It would cut $17.3 billion in Medicare, Medicaid and welfare over three years.

When the spending votes were finished, Chairman Robert J. Dole (R-Kan.) announced that tax voting will start today.

Dole made clear he is not planning any dramatic action on so-called flat-tax proposals or on imposition of a wholly new tax, such as a big new energy tax.

Instead, Dole said, he wants to raise new revenues by smoothing out the "proliferation of special privileges" and "special tax relief at the expense of the general" which "undermines confidence in the system" and creates "taxpayers' resentment over the perceived unfairness of the tax system."

The flat-tax concept would be the subject of hearings later on, he said, after the deficit-reducing proposals were completed.

Dole spent much of the day caucusing with other committee Republicans in the hope of working out a complete tax package before beginning today's voting on new revenues.

Dole said the discussions were focusing on creating a tax system "fairer, simpler and easier to administer and comply with." Among areas for possible change, he listed revision of safe-harbor leasing and of pension deductions for the highly paid, taxation of life insurance, changes in breaks for tax-exempt revenue bonds, and minimum taxes on business.

Earlier in the day, he told reporters after the White House signing ceremony on the Voting Rights Act extension that the minimum tax on business was "a very sticky" problem, that withholding of taxes on interest and dividends was back on the table (it had been declared dropped earlier), that he is looking at a tax cap on deductions for health-insurance premiums and that airport-airways and new excise taxes may still be considered.

House Minority Leader Robert H. Michel (R-Ill.), in a remark after conferring with Treasury Secretary Donald T. Regan, said there were "a lot of rinky dink things we can put together" to achieve the $20.9 billion in new revenues.

In finishing work on the three-year package of benefit cuts, the committee agreed to let ex-servicemen who are honorably discharged but decline to reenlist get up to 13 weeks of unemployment benefits. The benefits would begin after a four-week waiting period if the ex-serviceman can't get a job and had been in service at least two years.

Although Sen. Bill Bradley (D-N.J.) complained that this treats the ex-servicemen more harshly than other unemployed, who usually get at least 26 weeks, he agreed to Dole's proposal that the provision be accepted as a compromise. Benefits for ex-servicemen who decline to reenlist had been repealed last year in the presidential budget blitz.

In other action, the committee delayed until the second half of 1983 penalties on states that don't get their Medicaid error rates down to 3 percent, and allowed error rates of 4 percent for Aid to Families with Dependent Children in fiscal 1983, dropping to 3 percent thereafter.

These changes and a few others actually reduced by about $700 million over three years the savings from the welfare and health cuts that had been approved initially last week, but reestimates for the total cut put the final figure at $17.3 billion from fiscal 1983 through 1985.

An amendment by Sen. Daniel Patrick Moynihan (D-N.Y.) to permit Social Security student benefits for anyone enrolling in college by October (instead of the May 1, 1982, deadline) was opposed by Dole and lost, 12 to 5.