The Senate Finance Committee voted yesterday to let the states force welfare clients to "work off" their benefits at special jobs paying below the federal minimum wage in most cases.

The provision, strongly opposed by many welfare organizations and by the Carter administration, was one of a package of welfare-law changes ordered reported to the floor by an 8-to-3 vote of the committee.

Another major provision, also opposed by the Carter administration, was Sen. Daniel Patrick Moynihan's $1 billion "fiscal relief" special welfare payment to he states and the cities. The administration has not budgeted the money for this year and wants fiscal relief for the states on welfare to come as part of its overall revision of the welfare system.

Although the welfare package contains some provisions the administration likes, like a future ceiling on payments for foster-care of children and a major authorization of payments to low-income families who adopt homeless children, much of the bill contains Carter-opposed provisions. They include changes in the work incentive program that the Department of Health, Education and Welfare considers worthless, changes in the amount of earned income that is disregarded in computing how much welfare a person can get, a numerous other changes in the law.

Although the Carter administration couldn't prevent approval of the bill, it did block on an 8-to-8 tie an attempt by chairman Russell B. Long (D-La.) to combine some of the committee welfare changes in a single bill with measures to rescue the Social Security system. With the bills separate, the President could veto the welfare measure if it reaches his desk. Tied together, a veto would be much more difficult because new Social Security financing is so urgently needed this session.

Besides opposing the "work off" provisions and many others on policy grounds, the administration fears that if Congress passes a welfare bill this year, it will sap its resolution for taking on the big Carter welfare-revision package next year.

The provision on "working off" welfare benefits revives an old program which has long been a pet of the Finance Committee.

The "work off" provision (often called "workfare") applies only to families on Aid to Familes With Dependent Children - the program supporting mothers and (depending on state law) unemployed fathers and their minor, dependent children. The program pays for the support of both parents and children.

Under the proposed "workfare" program, state or local welfare authorities could require adults receiving benefits under the AFDC program to work off hteir benefit payments.

They would be paid the locally prevailing wage for such work (cleanup, yardwork child-center work and the like) or the state minimum wage, whichever is higher. But in many states this is lower than the federal minimum wage.

The jobs would have to meet health and safety standards, provide workmen's compensation protection, serve a useful purpose, and could not be used to displace other workers normally employed in the area at regular wages.

If the mother and father were ill, crippled, had a child under six or were caring for an invalid, they could not be forced to work for their welfare checks. It is estimated that about 1.5 million to 2 million adults on AFDC would be potential workers under the program - if all states put it into effect.

The aim of the "workfare" concept is to push able-bodied welfare clients into the habit of useful labor, but the American Public Welfare Association, Center for Community Change and Carter administration all strenuously opposed the provision yesterday.

Leonard Lesser, a welfare expert with the Center for Community Change, said, "I think that's terrible. People should work at jobs like anyone else. Just because they happen to be poor they shouldn't be treated like second-class citizens. They should be given jobs at the same wage as anyone else."

The objection to forcing persons to take jobs paid at less than the federal minimum wage and the suspicion that the jobs would merely be dead-end, yard-work positions leading nowhere in the long-run also is part of the Carter administration's objections. An administration spokesman said the proposal does not provide any of the training and support services that would enable affected persons to get permanently off welfare. Some unions also oppose "workfare" as providing a pool of potential low-wage persons to undercut the regular wage level.

In past years, Long has said he believes many strong and able-bodied welfare clients, unable to get normal jobs, would welcome the chance to do something useful - and the local community would at least get some work for the money it is paying out.