Upon retirement, Cloutier was hired as an assistant coach for the Nordiques' AHL affiliate, the Cornwall Aces. While coaching the Aces, Cloutier also served as a part-time goaltending coach for the Nordiques. In 1995 the Nordiques moved west to become the Colorado Avalanche and Cloutier moved with the team, becoming the full time goaltending coach. Midway through the 1995-96 season, Cloutier was promoted to assistant coach with the Avalanche. During his time as a coach in Colorado, Cloutier helped the Avalanche win the Stanley Cup in 1996 and on Head Coach Bob Hartley staff in 2001. He spent a total of 12 seasons as an assistant coach with the Avalanche concluding in 2009.
Cloutier had an impressive career starting in the QMJHL. In 1977-78, just his second year of major junior hockey, Cloutier played in 71 games, going 46-17-7 and helped lead the Draveurs to the Memorial Cup. The next season he played 72 games going 58-8-6 and captured the Jacques Plante Memorial Trophy for best goaltender in the QMJHL and again leading the Draveurs to the Memorial Cup.
The following season, Cloutier was selected in the 3rd round of the 1979 NHL Entry Draft by the Buffalo Sabres with the 55th pick overall where he played up until the end of the 1988-89 season. He spent the 1989-90 season and part of the 1990-91 season with the Chicago Blackhawks before finishing his goaltending career after four years with the Quebec Nordiques.