The Titans announced the moves Wednesday.
The 6-foot-4, 240-pound Burnett has played in 22 NFL games after signing with Oakland as an undrafted free agent. The younger brother of former University of Tennessee player Kevin Burnett, the linebacker played 38 games in college at Nevada.
The 6-5 Sutton played in college at South Carolina as a defensive end and signed with Tampa Bay after the 2014 draft. He was waived at the end of training camp.