The Jets cut Zappe on Saturday, Rich Cimini of ESPN.com reports.
Zappe signed with New York on a reserve/future contract in January and entered training camp with a legitimate shot to win the No. 2 QB job. However, he struggled during preseason play, completing just 14 of 23 passes for 135 yards with no touchdowns and two interceptions. Zappe's departure means that either Cade Klubnik or Brady Cook will serve as Geno Smith's backup when the regular season kicks off.