The club will announce other cuts later Monday afternoon.
Gutierrez, 26, has spent time on the rosters with the Kansas City Chiefs and New England Patriots. Gutierrez played in one game last season with the Chiefs, throwing only one pass in all of 2009.
The play of rookie Dan LeFevour on Saturday against the Arizona Cardinals may have played in the club's decision to cut Gutierrez. LeFevour posted a 129.2 passer rating against the Cardinals, while completing 10-of-12 attempts for 100 yards and a touchdown.
LeFevour had struggled during training-camp workouts, but appears to be progressing. Once backup Caleb Hanie returns from a shoulder injury, the club will have to make a decision on whether to keep LeFevour because the Bears still have four quarterbacks on the roster.
It's unlikely the club will keep four quarterbacks, so if it decides it wants to retain LeFevour, the Bears will have to risk putting him on the practice squad.
The club faces a final mandatory roster reduction deadline on Sept. 4 to 53 players.
Michael C. Wright and Jeff Dickerson cover the Bears for ESPNChicago.com and ESPN 1000.
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