The left-handed Seay will attempt to recover from an injury to his pitching shoulder without surgery. He is expected to be sidelined six weeks.
Miner, a right-hander, has been hampered by tendinitis in his pitching elbow.
Both players will remain in Florida for rehabilitation. The moves made Saturday are retroactive to Friday.
The Tigers also optioned outfielder Wilkin Ramirez and left-hander Daniel Schlereth to Triple-A Toledo and assigned pitchers Enrique Gonzalez and Phil Dumatrait and catcher Max St. Pierre to minor league camp.