The White House has quietly fired three members of the Renegotiation Board, the small agency that is supposed to recover excessive profits from defense contractors. The new chairman and two replacements have been among the board's severest critica.

White House deputy counsel Margaret McKenna phoned acting chairman Rex M. Mattingly and member Christopher U. Sylvester about 5 p.m. Friday to say that President Carter had accepted their resignations effective immediately. She left a message accepting the resignation of member Norman B. Houston, who is in Africa.

Mattingly had been an oil distributor and Republican national committeeman and state chairman in New Mexico.

Sylvester, after working 20 years for Sen. Milton R. Young (R-N.D.), wanted a change. Young has said that he asked President Ford to find "something appropriate" - and Ford put Sylvester on the board.

Houston came to the board from the Department of Health, Education and Welfare, where he was a deputy assistant secretary.

Earlier Friday, Carter met with the three men he told he intends to nominate:

Goodwin Chase, 65, a former Tacoma, Wash., banker who has been on the board since 1973. From the start, he has dissented repeatedly - and often alone - from actions and non-actions that, he protested, were needlessly costing the taxpayers hundreds of millions of dollars.

William F. McQuillen, 33, He worked for 2 1/2 months in the Carter campaing after spending 1 1/2 years as counsel of the House Banking subcommittee that monitored the board and drew up and pressed legislation to overhaul it.

Harry R. Van Cleve, 53, general counsel of the Cost Accounting Standards Board, an independent agency of Congress headed by Comptroller General Elmer B. Staats. Van Cleve has had 16 years of government prosgrement and accounting experience, including four years as general counsel of the General Services Administration.

The White House announced yesterday that Carter had designated Chase to be chairman of the board, but did not announce either the dismissals or the selection of McQuillen and Van Cleve. If the Senate confirms the appointments, two vacancies will still exist on the board.

Former chairman Richard G. Holmquist resigned at the end of last year. He was an out-of-work Lone Star Industries executive when President Ford tapped him in 1974.

The board long has been a favorite target of Adm. H. G. Rickover, who is known as the father of the nuclear Navy and who has been an inspirational leader to Carter.

In 1974 testimony, Rickover told the House subcommittee that the board was "probably the biggest sieve in government" and remained a refuge for "political hacks."

Since its creation 25 years ago, Democratic and Republican Presidents alike - with the exception of Carter - have made the board a snug harbor for well-connected politicians.

Former members included two former congressmen and a governor, all of whom had lost bids for re-election. President Nixon appointed two former GOP national committeemen and state chairmen, Mattingly and D. Eldred Rinchart of Maryland.