The Fairfax County Board of Supervisors angrily cut off the county's payments to the Northern Virginia Health Systems Agency yesterday, charging that the nonprofit health planning agency had opposed the county once too often.

The board's decision, which will lop off about 7 percent of the regional agency's $325,000 annual operating budget, came in response to the agency's threat to sue Fairfax Hospital in an effort to block the hospital's planned heart transplant program.

The hospital's application to start the first heart transplant program in the Washington area was approved March 28 by Virginia Health Commissioner James B. Kenley. HSA officials, who had opposed the program, said last week they would challenge Kenley's decision in a suit in Fairfax County Circuit Court.

"If it were up to HSA, doctors in Fairfax Hospital would still be performing operations with a pen knife rather than a scalpel," said County Board Chairman John F. Herrity. He introduced the motion to cut off the agency's funding, with only Supervisor James M. Scott (D-Providence) abstaining.

In other actions yesterday, the county board:

*Gave final approval to a $1.4 billion fiscal 1987 budget that includes a 4-cent reduction in the real estate tax rate to $1.35 per $100 of assessed value and a 4 percent cost-of-living increase to the county's 7,000 teachers.

*Asked the county School Board to consider televising its meetings, held Thursday nights.

The HSA's decision to attempt to block Fairfax Hospital from performing heart transplants was the latest, but not the first, time the agency has crossed the county's politicians. In 1984, the agency opposed building any new hospitals in the western portion of Fairfax County.

The county board, disregarding the recommendation, endorsed a 160-bed hospital for the Fair Oaks area.

HSA also has opposed a board-backed program for kidney stone victims, who currently must journey to Charlottesville for treatment.

HSA maintained that because Richmond's Medical College of Virginia and Baltimore's Johns Hopkins University already offer first-rate heart transplant programs, another facility in the Washington area is unnecessary. The agency warned that it could strain the already limited local supply of donor hearts, and contended that Fairfax Hospital, which has limited experience with operations involving immunosuppressant drugs used in transplants, was not well qualified to perform heart transplants.

Mark H. Epstein, associate director of the health agency, said that the cutoff would not have a major impact. The agency receives most of its money from federal grants, as well as contributions from most Northern Virginia localities.

The fiscal 1987 budget approved yesterday did not meet teachers' demands for an across-the-board 8.8 percent pay increase, and brought an angry response from teachers.

In a news conference yesterday, Donna Caudill, president of the Fairfax Education Association, which represents most of the county's teachers, said: "Jack Herrity and his supervisors are making a big mistake if they think they can buy school employes off with vague promises instead of dollars in our pockets."