Grappling to balance its budget in the face of state aid cuts, the Arlington County Board voted unanimously yesterday to cut $2.3 million from this year's $342.9 million budget and to raise $600,000 in 1991 by increasing the business license tax on commercial property rents.

County Manager Anton S. Gardner had suggested a further increase in the business license tax, but the board said it would cut $600,000 more next month, including $300,000 from the school budget.

"We should cut expenditures," said board member Mary Margaret Whipple, a Democrat who is running for reelection to the board Nov. 6. Whipple's challenger, Republican-backed Monte Davis, has criticized the county government for what Davis calls wasteful spending.

Whipple called the $2.3 million in cuts "manageable reductions . . . with minimal impact on services."

More than a dozen permanent and temporary jobs ranging from clerks to inspectors will be left unfilled for various amounts of time. Some capital improvement projects will be put off until later years. These include the Chain Bridge bike trail, landscaping along Columbia Pike and improvements to the police radio system.

The cuts stem from a $287 million cut in state aid to counties and cities announced this fall.

The $300,000 in school cuts will be difficult to absorb, School Board member Dorothy Clarke said after the meeting. Until now, the schools had been shielded from the effects of state cuts, but the system has been hit hard by an unexpectedly large number of new students.

"We're really at the bare bones. You have to think in terms of programs" for cuts, she said. But Clarke said the reductions might come from programs such as staff development rather than ones that immediately affect students.

The business license tax rate will rise to 43 cents per $100 of gross receipts, from the current 28 cents. Residential properties would not be affected.

Board members said the increase will allow the county to give child-care subsidies to more poor families, indirectly helping businesses by keeping workers in the labor force.

The tax boost was criticized by James R. Cooke, a representative of the Arlington Chamber of Commerce, who said the measure would hit the real estate industry hard when it is already reeling from the slump in the regional economy. The tax is particularly painful because it taxes overall receipts rather than just profits, he said.

Though it did not relish yesterday's budget cutting, the board was quick to remind listeners that the overall fiscal health of the county is good and that things are worse for other jurisdictions in the Washington region and throughout the country.

An even tighter fiscal picture is predicted for next year. Revenue is expected to grow by 3.4 percent, to $351.5 million, but full funding of planned programs and increases in areas such as rents, salaries, equipment costs and health insurance premiums would cost $384.9 million. The board will conduct a public hearing Nov. 17 before it adopts budget planning estimates for next year.