Cloutier played junior hockey in the Ontario Hockey League (OHL) for four seasons with the Sault Ste. Marie Greyhounds and Guelph Storm, making two Memorial Cup appearances in 1993 and 1996. Following his second OHL season, he was selected 26th overall by the Rangers in the 1994 NHL Entry Draft. He began his professional career spending time in the minor leagues with the Rangers' American Hockey League (AHL) affiliates, before joining the NHL team full-time in 1998–99. After three seasons playing within the Rangers organization, he was traded to the Lightning, where he spent one-and-a-half years.