Shaw made his professional debut in the 1982–83 season, appearing in two games with the Quebec Nordiques, earning no points.
In 1984–85, Quebec assigned Shaw to the Fredericton Express of the AHL, where he had 13 points in 48 games, earning a promotion to the Nordiques.
On September 30, 1987, the Nordiques traded Shaw and John Ogrodnick to the New York Rangers for Jeff Jackson and Terry Carkner.
[1] Shaw missed the majority of the 1989–90 season due to a shoulder injury in a game against his former team, the Quebec Nordiques, on November 2, 1989.
Shaw appeared in 12 games with the Edmonton Oilers, scoring a goal and an assist, as well as a –8 rating, before being traded to the Minnesota North Stars for Brian Glynn on January 21, 1992.
Shaw finished the 1991–92 season with the Minnesota North Stars, earning seven assists in 37 games, helping the team qualify for the playoffs.
Shaw had a good playoff with the team, scoring two goals and four points in seven games as the North Stars lost to the Detroit Red Wings in the first round.
In the 1995–96 season, Shaw appeared in 66 games, earning 12 points, as he helped the Tampa Bay Lightning clinch their first-ever playoff berth.
Shaw appeared in 57 games with Tampa Bay in 1996–97, registering 11 points, as the club failed to make the playoffs.
He spent some time in the International Hockey League (IHL), playing in 26 games with the Las Vegas Thunder, as he had 19 points.