Selected by the Washington Capitals 61st overall in the 1985 NHL Entry Draft, Murray played parts of two seasons for the Capitals. At the end of the 1990–91 season, he was claimed by the Minnesota North Stars and was traded the very next day to the Winnipeg Jets. Murray would spend most of his time in the Jets' minor league affiliates; first the Moncton Hawks for three seasons, and then the Springfield Falcons for eight, for which he is the career games leader and longtime captain.