On its Web site, the team said it still owes Ortiz more than $20 million for the next two-plus seasons. He signed a four-year, $33 million dollar contract last season, when he went 5-11 with a 6.89 ERA.
In 2006, the 32-year-old right-hander was 0-5 with a 7.54 ERA in 22 2/3 innings. He was designated for assignment June 13.
Mulholland, 43, a left-hander who has pitched for 11 teams, had no decisions. His ERA was 9.00 in three innings of relief.
He had been on the disabled list for much of the season with an inner ear infection.
"It's tough to part ways with a classy guy like Terry Mulholland," said Manager Bob Melvin, who caught Mulholland's first-ever big-league game in 1986. "We wanted to give him an opportunity to go somewhere else."