A hard-nosed right-winger, Mulvey played junior hockey with the Edmonton Oil Kings and the Portland Winter Hawks. He was selected in the 1978 NHL Draft by the Washington Capitals and played for parts of three seasons with the Capitals. Prior to the 1981–82 NHL season, he was sent to the Pittsburgh Penguins as compensation for the Capitals signing of Orest Kindrachuk. He would later be claimed on waivers by the Los Angeles Kings during the middle of the season. His older brother, Grant Mulvey, had a long career with the NHL's Chicago Black Hawks.