Craig Coxe was selected in the fourth round, 66th overall in the 1982 NHL Entry Draft by the Detroit Red Wings. As a junior, he played two years with the Belleville Bulls of the OHL. While it was apparent he had some offensive abilities, it was his size and willingness to mix it up that drew the attention of the pro scouts. Coxe averaged a point per game in his last junior season, scoring 45 points in as many games.

With the Detroit Red Wings already carrying an abundance of toughness and large forwards, the Red Wings moved Coxe's rights to the Vancouver Canucks. In 1984-85, Coxe played 62 games with the Fredericton Express of the AHL, scoring 15 points while accumulating 242 minutes in penalties. The Canucks were impressed by his tenacity and they called him up for nine games.

In 1985-86, Coxe secured a roster spot with the Canucks, appearing in 57 games. The following season he dressed for 64 games, scoring five goals and 17 points. Coxe also had brief stays in Calgary and St. Louis before playing his last NHL season in northern California with the San Jose Sharks in 1991-92.

During his relatively brief NHL career, Coxe became known as one of the league's premier fighters. He had several classic encounters against the likes of Edmonton's Dave Semenko and Detroit's "bruise brothers" Bob Probert and Joey Kocur. Coxe always looked upon that aspect of the game as being a service he was asked to provide, and was quite willing to do so. He says the toughest time for him was when he was traded by the Canucks to the Calgary Flames.

Coxe continued to play professional hockey in the minor leagues until the age of 36 when he retired after the 1999-2000 season while with the San Antonio Iguanas of the CHL. For recreation, Coxe enjoys biking and rollerblading, which led him to playing two seasons of organized summer roller hockey with the Phoenix Cobras and the Vancouver Voodoo in 1994 and 1995.