The New York Giants placed quarterback season roster limit of 53 players.
Clayton caught 80 passes for 1,193 yards and seven scores for the Buccaneers during 2004, his rookie season. He remained with Tampa Bay through 2009, but caught just two passes for 19 yards for the Giants last season.
Watson, who played in 62 games for Arizona from 2006-10, was signed in early August.
Linebackers Phillip Dillard and Adrian Tracy, and punter Matt Dodge, all 2010 draft choices, were waived Saturday.
Also waived by the Giants were quarterback Ryan Perrilloux, running backs Andre Brown and Charles Scott, tight end Christian Hopkins, wide receiver Darius Reynaud, tackles Jamon Meredith and Jarriel King, center Jim Cordle, defensive ends Ayanaga Okpokowuruk, Craig Marshall, Alex Hall and Justin Trattou and Dwayne Hendricks and defensive backs Joe Burnett, David Sims and Jerrard Tarrant.
Safety Brian Jackson was waived/injured with a hip problem.