The Arlington County Board refused yesterday to budge from its insistence that the county's schools cut their planned spending, directing the school board to come up with specific cuts into programs that some educators say are vital.

Members of the County Board told school board members at a joint meeting that they were not satisfied with the school board's proposed $59.8 million budget for fiscal 1982 -- an 11.5 percent increase over last year and $3.5 million more than the County Board had previously said it would fund.

County Board members Walter Frankland and Dorothy Grotos -- the panel's most conservative members -- were adamant that school authorities had not tried hard enough to meet the board's budget guidelines. "I find it hard to believe that the proposed budget does not have places where cuts could be made," Grotos said.

In occassionally acerbic rebukes, Frankland accused the school board of deliberately misrepresenting its budgets, citing increasing cost overruns in the past two years as an indication of fiscal trickery. "If I thought money were the solution," he said, "the school board would have an open checkbook as far as I'm concerned."

But the County Board was in no mood to hear of fiscal overruns, having only last week reduced the country's real estate tax rate by 16 cents, a move some authorities believe could imperil some county services threatened by Reagan administration reductions in federal assistance.

School board members yesterday defended the increases in their proposal, saying the school system is burdened by recent salary agreements and the inflated costs of Social Security, hospitalization and utilities. Besides, said school board member Torill B. Floyd, "Arlington County can support the kind of budget the superintendent has come in with."

Grotos and Frankland would not be swayed, however. "Every time we go through this exercise we end up with the same problem -- that the board doesn't say how cuts would affect programs," chided Frankland. "The problem is they have so much money over there they can't tell how it's going to hurt.

"If every department went 100 percent over the recommended budget, the county government would be totally out of control," he said.

"The recommended guideline," responded Floyd, "has never been as unrealistically low as this year."

The County Board gave the school board no specific deadline for its budget revision. But the County Board is scheduled to approve its budget for fiscal 1982 on April 25.

Under Virginia law, the County Board can set the total amount of school spending, but cannot specify how those funds are to be spent. That function is the responsibility of the school board, whose members are appointed by the County Board.