The Titans announced the moves Thursday.
The 6-foot-4 Staples joined the practice squad in September and was on the Cleveland practice squad at times during the past two years. He was undrafted out of Illinois where he played defensive end. He fills the roster spot opened when the Titans released linebacker James Anderson earlier this week.
Smallwood was a seventh-round draft pick by Atlanta who was waived after the Falcons' training camp. He started three years at Connecticut.
AP NFL website: www.pro32.ap.org and www.twitter.com/AP-NFL