The D.C. City Council, apparently clearing the way for some property tax relief for city homeowners, voted yesterday to trim $7.5 million from proposed supplemental budget requests by Mayor Walter E. Washington.

The Council overrode a series of vetoes by the mayor, who had sought to restore funds that the Council had previously cut from his proposals for increased spending both this year and next.

Both the Council and the mayor already have proposed their own plans for property tax relief. No action on either of the two plans was taken yesterday.

The largest cut made by the Council as it overrode the mayor's vetoes yesterday was a $4 million probably can be saved as a result of a recently announced effort to reduce overpayments to welfare recipients and remove ineligible families from the city's relief rolls.

Mayor Washington had vetoed the $4 million welfare cutback, contending that it may jeopardize plans for a 5 per cent increase in welfare benefits. The Council, while overriding the veto, instructed the mayor, nevertheless to carry out the proposed 5 per cent boost in benefits.

While insisting on many of its previous budget cuts, the Council allowed the mayor to restore some of the funds he had sought, including $704,100 for street lightning. Without the appropriation, the mayor had argued, the District government might be forced to reduce the number of street lights in some areas of the city.

The Council votes yesterday were its final action on an $11.2 million supplement to the city's $1.1 billion budget for the current fiscal year, and on a $7.7 million amendment to the city's proposed $1.2 billion budget for the 1978 fiscal year. The latter is pending in Congress. Both supplemental appropriations require congressional review.

The Council previously had proposed a $16.6 million property tax relief plan. It would allow homeowners to deduct $6,000 from their property tax assessments before the city's tax rate of $1.83 for each $100 of assessed valuation would apply. It is intended to save every homeowner more than $100 in annual property taxes.

Councilman Marion Barry, chairman of the finance and revenue committee, said after yesterday's Council votes that the Council's budget cuts and other possible savings will allow and city to carry out the proposed tax relief plan.

Mayor Washington Proposed his own property tax relief program last week, including a plan for special tax breaks for the elderly. The mayor's proposal, described as a "circuit breaker" system, would limit property taxes by imposing a ceiling equivalent to a percentage of a homeowner's income.

Under the mayor's proposal, the ceiling on property taxes would range from 3 per cent for households with incomes of $5,000 to $9,999 to as much as 7 per cent for households with incomes of $25,000 or more. For persons over 65 years old, the ceilings would be halved. The mayor's tax relief plan also would provide tax breaks for tenants who rent their homes and for owners of commercial property.