Knighton tweeted about the cut Monday morning:
Knighton, an eight-year veteran, did not play a single defensive snap in New England's preseason 19-17 win over the Carolina Panthers on Friday. He acknowledged after the game that he was uncertain about his place with the team.
"You're always concerned when you're not playing," he said. "I prepared myself to play, the coaches made the decisions on who they wanted to play, and I'm not going to ask any questions or make any excuses or look for any explanation. I'm just going to get dressed, get back on the plane and see what happens."
The 6-foot-3, 355-pound Knighton signed a one-year contract in April. He was expected to complement returning starters Malcom Brown and Alan Branch while buying time for third-round pick Vincent Valentine.
"Just didn't work out," Patriots coach Bill Belichick said Monday. "He came in, worked hard, lost weight, got in good condition, tried to do the things we asked him to do. Just other people ahead of him."
Knighton, who played for Jacksonville (2009-2012), Denver (2013-2014) and Washington (2015), had talked about how playing in New England's defense with two-gap principles was a change for him.
A return to the Redskins doesn't appear to be in the cards, with a team source telling ESPN's Britt McHenry that there isn't much interest in Knighton at this time.
ESPN's Mike Reiss contributed to this report.