Canty and Beckum are both recovering from offseason knee surgery and will not be eligible to play until after the first six games of the season.
The two Giants were on the PUP list in training camp and have not practiced. The Giants could have used Canty, who started 16 games in each of the past two seasons and was a big part of the defensive line.
Canty said he did not suffer any setbacks in his rehab and he thought he was close to returning.
"I stand by the position my knee is better than it was November, December, January of last season," Canty said. "But ultimately this was a decision that was made in the best interest of the football team."
"I feel like I'm close," Canty added. "Obviously saying that my knee is in better physical condition, not just the way it feels but anatomically it's better than what it was. They did not feel comfortable putting me back on the football field with full confidence that I would be able to compete at a high level."
Beckum tore his ACL during the Super Bowl win over the New England Patriots and needs more time to strengthen his knee.
The Giants also placed offensive lineman Brandon Mosley, a fourth-round pick, on injured reserve with an ankle injury.
And to reduce the roster to 75, the Giants waived cornerbacks Antwaun Molden and Brandon Bing, tight ends Ryan Purvis and Chris Hopkins, defensive tackles Carlton Powell and Oren Wilson, safeties Chris Horton and JoJo Nicolas, receivers Julian Talley and Brandon Collins and running back Joe Martinek.
With Canty not eligible to return until at least mid-October at the earliest, the Giants will start Linval Joseph and Rocky Bernard at defensive tackle. Marcus Thomas, Markus Kuhn and Dwayne Hendricks are currently behind those two.
Canty hopes he will be ready when he is eligible to be activated off the PUP after the first six games. But it will be up to the team to clear him.
"I don't have a crystal ball," Canty said. "If you were to ask me would I start the season on PUP, I'd say there's no chance. But here I am."
"This obviously was something that needed to be addressed," he added of the surgery. "I played a third of the season last year including the postseason with this particular ailment. It is tough to officially know that I am not going to be starting the 2012 season."