A club statement revealed that Cooper and physio Paul Chappell would leave "as part of a restructuring of the football staff".
The former Aberdeen and Rangers midfielder, who managed County from 1996 to 2002, returned to the club in November 2012.
Manager Derek Adams added: "I would like to thank Neale and Paul for their assistance while at the football club. I wish them every success in the future."
Cooper's son, Alex, remains in the first-team squad.