The Navy has cut off the $21,000-a-year retirement pay of Arthur James Walker, the retired Navy officer convicted last month of espionage.

A Navy spokesman said Walker's $1,755-a-month payments ended automatically after his Aug. 9 conviction on seven espionage counts in federal court in Norfolk, under a federal law barring retirement pay for armed services personnel convicted of espionage.

J. Brian Donnelly, one of Walker's court-appointed lawyers in the five-day trial, said in an interview that the cutoff of funds has left Walker's wife Rita destitute, with virtually no other means of support.

Walker, 50, was convicted of passing classified documents from his job at VSE Corp., a Chesapeake, Va., defense contractor, to his brother John Anthony Walker Jr., who is charged with being a Soviet agent. Arthur Walker, who retired as a lieutenant commander in 1973 after 20 years in the Navy, lost his job as an engineer at VSE after he was arrested in May.

Under the law, John Walker, 47, who retired as a Navy chief warrant officer in 1976, would lose his $1,207-a-month retirement pay if convicted. John Walker's friend Jerry Alfred Whitworth, 46, who retired in 1983 as a senior chief radioman, would also lose his pay, amounting to $1,206 a month, if convicted, Navy officials said.

The fourth person charged in the alleged spy ring, John Walker's son, Michael, has already lost his Navy pay and allowances. Under Department of Defense rules, Michael Walker, a seaman aboard the aircraft carrier Nimitz, was denied his $1,000-a-month pay and allowances when he was arrested in May.

Sentencing for Arthur Walker, who faces the possibility of three life terms plus 40 years in prison and a $40,000 fine, is set for Nov. 12.

John Walker is scheduled to go on trial in Baltimore Oct. 28; Whitworth is to stand trial in San Francisco in November. Michael Walker's trial will begin after his father's ends.

In San Francisco yesterday, U.S. District Judge John P. Vukasin ruled that the death penalty cannot be applied in Whitworth's trial. After two hours of hearings in which a lawyer for the Washington Legal Foundation argued that spies should face the death penalty, Vukasin said he was ruling "extremely reluctantly" that related judicial decisions prompted him to deny the motion.

"Even though I want to allow the death penalty , I should not, so I shall not," the judge said.

Similar appeals by the same group were rejected by judges in the Walker cases. Federal prosecutors have said they believe there has been no valid federal death penalty for espionage since 1972, when the Supreme Court invalidated a wide array of capital punishment statutes.