Branch was cut by Buffalo on Aug. 24, one day after being arrested on a drunken-driving charge. He spent the previous four seasons with Arizona after being drafted in the second round in 2007, then played two years for Seattle. He started 47 of his 94 games and had eight sacks. With Buffalo last year he had 39 tackles in 16 games.
Skinner signed with the Patriots as an undrafted rookie from Mississippi State on May 27. He had one start in seven games and made 10 tackles on defense and three on special teams. His release comes after the Patriots traded for linebackers Akeem Ayers from Tennessee last week and Jonathan Casillas from Tampa Bay on Tuesday.