Prince William County Executive Clinton B. Mullen resigned yesterday in a one-sentenced letter that masked the bitterness of his departure.

The Board of Supervisors accepted the resignation with one dissenting vote. That vote, cast by James Byrd, was in protest of the severance agreement worked out with Mullen in closed session.

Mullen, who was out of town yesterday and could not be reached, wrote: "On the understanding that I will receive three months severance pay in an amount equal to what I would have been paid for the months of April, May and June of 1978, and pay for unused leave, I hereby submit my resignation as county executive of Prince William County, Virginia, effective the close of business, March 31, 1978,"

Board members, including those who openly had sought Mullen's dismissal, refused to discuss the reasons behind his departure after 3 1/2 years.

Byrd said, "No comment, I wish him well in his new endeavors."

"I didn't want to get rid of Mr. Mullen. Mr. Mullen wanted to leave," said Chairman Donald L. White.

Mullen had indicated last month when rumors that he would be removed became public that he was being forced out. "This can be the loneliest job in the world. There's a thing in this business that you're only secure until the next board meeting," he said.

Mullen, who holds a bachelor's degree from Columbia and a master's degree from the University of Pennsylvania, was county executive in Powhatan County, Va., before moving to Prince William. Neither of his Prince William predecessors had lasted a year in the politically tumultuous county.

Mullen's tenure saw the Prince William government move from a rural past into a more urban present and there was major improvement in the county's financial condition.

Mullen, 45, a formal, aloof person, never quite fit in Prince William County, according to some staff members. Several board members appeared to have developed personal dislike for Mullen and Mullen seemed to have trouble disguising his disdain for some board members.

The fight over the defeated proposal to move the county courthouse from the independent city of Manassas to Independent Hill and a dispute over his salary were the final elements in his departure.

The board cut Mullen's pay after some supervisors said they were not aware that he had received $7,000 in cost-of-living and merit raises on his beginning salary of $28,000.

During the courthouse battle, planning director Jeff Middlebrooks, who was working closely with the board majority seeking to move the county seat, submitted a letter of resignation in which he attacked Mullen for lack of support and claimed that staff morale was low.

When the board refused to accept Middlebrooks' resignation, Mullen's position became increasingly tenuous.

After accepting Mullen's resignation yesterday the board named Assistant Executive Virginia Young as acting county executive effective immediately. The board also directed that the county advertise for applicants for the county executive's job.