Both players are now free to sign on with a team of their choosing.
Michael, 24, is a former second-round pick of the Seahawks back in 2013. He was traded to the Cowboys at the start of the season for a conditional seventh-round pick.
He was in the third year of his four-year, $3.374 million rookie contract when the Cowboys cut him on Tuesday.
This season, Michael has ran for 51 yards on 15 carries (3.4 YPC) to go along with one reception for two yards receiving and no touchdowns.
Swearinger, 23, is a former second-round pick of the Texans out of South Carolina back in 2013. He had two years remaining on his four-year, $3.49 million rookie contract before the Bucs cut him loose on Tuesday.
This season, Swearinger has appeared in seven games for the Buccaneers and recorded 12 tackles and a fumble recovery.