After his most recent transgression, Burress was suspended for the final four games last season and placed on the reserve/non-football injury list after he accidentally shot himself in the leg at a local night club.
The move came three days after his hearing on the incident was postponed until June 15 to give his lawyers time to negotiate a plea agreement.
Burress, 31, surrendered to authorities and was arraigned on two felony weapons charges, and was fined and suspended for conduct detrimental to the team.
"I am an optimist, and I believe most situations can be worked out," Giants' General Manager Jerry Reese said in a statement late Friday. "We hung in there as long as we could in hopes that there could be a resolution to this situation other than the decision we made today."