The Saints also released defensive end Hau'oli Kikaha, a former second-round pick, as they began paring their roster down to 53 players.
Vereen suffered an unspecified injury in New Orleans' final preseason game on Thursday night. He was already on the roster bubble because he plays a similar runner/receiver role to that of Saints starter Alvin Kamara.
The Saints likely will lean on a combination of third-year running back Jonathan Williams and rookie running back Boston Scott to back up Kamara to start the season, while veteran Mark Ingram serves a four-game suspension for violating the NFL policy on performance-enhancing substances.
Vereen, 29, spent his first seven seasons with the New England Patriots and New York Giants before signing with the Saints in July. He had seven carries for 22 yards and nine catches for 41 yards with the Saints during the preseason.
Floyd and Tate also signed with the Saints late in the offseason -- both on Aug. 1 -- for what amounted to one-month training camp auditions.
Tate, 30, appeared to have the best shot at making the roster because of his kick-return abilities. But ultimately neither veteran was able to wedge his way into a crowded position group that also includes Michael Thomas, Ted Ginn Jr., Cameron Meredith, Tre'Quan Smith, Austin Carr and Tommylee Lewis.
Floyd, a former first-round draft pick of the Arizona Cardinals, will now look to resurrect his career with yet another team after spending time with four different teams -- the Cardinals, Patriots, Vikings and Saints -- over the last two years.
Floyd, 28, had just one catch for 16 yards in the preseason after catching just 10 passes for 78 yards with the Vikings last season.
Floyd's career was derailed in part by an arrest for extreme DUI in December 2016, which later led to a four-game suspension by the NFL. The 6-foot-3, 220-pounder showed some flashes of being a matchup problem in training camp, but Saints coach Sean Payton suggested that Floyd needed to lose some weight when he first arrived.
Tate, who spent his first nine seasons with the Patriots, Bengals and Bills, didn't catch a pass for the Saints in the preseason. But he returned three kickoffs for 99 yards and two punts for 7 yards.
Kikaha, 26, spent three seasons with the Saints, but he missed the entire 2016 season due to a torn ACL (his third, dating back to college). The 6-3, 246-pounder has eight career sacks and has started 11 career games.