The seven players waived included QB Brock Berlin, WR Josh Davis, RB Kay-Jay Harris, LB Corey Jenkins, CB Billy Parker, DE Chris Solomona and T Orrin Thompson.
Those moves mean Newson and Mitchell are done for the season, while Poole will be eligible to come after the sixth week of the regular season.
The moves left the Dolphins with 77 players, but the team has 10 NFL Europe roster exemptions. That means the team still has two moves to make before the 4 p.m. deadline.
"Ed Perry has done a good job for this organization for a long, long time," Saban said. "I have a lot of respect for him as a player and as a person. But from a business standpoint, it always makes sense to go with the younger guy."
The release of Perry came as a surprise not only to members of the media, but to Dolphins players as well.
"Nobody is ever a lock," said tight end Randy McMichael. "Pretty much everybody in Miami thought Ed Perry was a lock to be the long-snapper."