Murray was originally selected in the fifth round, 104th overall in the 1984 NHL Entry Draft by the New York Islanders after three years of junior in the Ontario Hockey League. At 16, Murray played for the Sarnia Bees in the Junior B where he notched 61 goals and 100 points in 57 games. As a rookie in Junior A, he suited up for the London Knights. About midway through his three-year career, Murray was traded to the Guelph Platers. In 1985-86 he appeared in 56 games for Guelph, scoring 27 goals and 65 points. In the playoffs he averaged a point per game as the Platers went on to win the Memorial Cup that spring.

The Philadelphia Flyers had obtained Murray from the New York Islanders at the 1986 NHL Entry Draft and he was commissioned to their minor-league affiliate in Hershey for the 1986-87 campaign. The following year Murray was called up for his one and only NHL contest. He played for another eight years in the minors before retiring. However, after a three-year absence, Murray returned to competitive hockey in 1999 at the age of 33 with the Knoxville Speed of the UHL. He played in 2000-01 with the Louisiana Ice Gators of the ECHL.