In the continuing shake-up of management at National Public Radio, the network's board yesterday forced its board chairman, Myron Jones, to resign, and accepted the resignation of the chief financial officer and assistant treasurer, Arthur Roberts.

The board, which is holding a special meeting to deal with the mounting financial difficulties and past mismanagement of the network, is expected to announce a forecast of its deficit for fiscal year 1983 today. The figure, according to public broadcasting sources, is said to be $9.1 million. Last week, NPR announced that an independent audit had found a $6.5 million deficit for the first seven months of the fiscal year. The original estimate for all of fiscal 1983 by then-NPR president Frank Mankiewicz in March was $2.8 million, later amended to $5.8 million.

Jones, who had been chairman of the board since last October, resigned over charges by NPR's interim chief operating officer, Ronald C. Bornstein, that he was "an obstacle to raising money and should go."

"Ron said he didn't feel we could get financing from the Corporation for Public Broadcasting if I remained as chairman and Steven Meuche remained as chairman of the finance committee," said Jones, who is also the executive director of Indian Education Training Inc., in Albuquerque. "I said if I thought I stood between NPR and solvency, I would resign but I don't think that is true. But I can't continue to chair a board in which the temporary chief officer can interfere that blatantly with the board. I resent that kind of interference."

Bornstein declined to reply.

Meanwhile, the board elected Donald Mullally, general manager of WILL in Urbana, Ill., as the interim chairman. Meuche, the general manager of WKAR in East Lansing, Mich., resigned as financial chairman but remains on the board. Wallace Smith, the general manager of KUSC in Los Angeles, resigned from the board effective Sept. 30. NPR's executive vice president, Thomas C. Warnock, has already announced his resignation, effective next month. Barbara Cohen, former chief of the news division, has already left NPR.

Mullally said that no one has been accused of any crimes, and refused to say whether Jones and Roberts shared any of the blame for the financial troubles of the network.

"I am not saying that," he said, declining to confirm the details of the Jones ouster. He added: "You have to recognize in any board conflict of all kinds. It is wrong to characterize it as a personal disagreement."

Jones declined to say if the costs of the interim management team were a reason for their friction. Bornstein is receiving $46,000 for part-time work from May 9 to Sept. 30, a fee that was approved by the board. Six other members of the interim group, hired by Bornstein, are reportedly receiving fees totaling $302,280. Their fees were approved by Bornstein, said Jones, who added, "he has the right to do it but it is not the custom at NPR."

Roberts, who joined NPR in 1979, will remain as a consultant until October. At a session with the board yesterday, Roberts said the recent auditors' report "contains numerous examples of errors and distortions." In response to the auditors' statement that $850,000 in payroll withholding taxes had not been sent to the federal government and had been improperly redirected, Roberts said the board and management was informed of "unpaid taxes" as early as Dec. 8.