He played the main character in the controversial 1985 Supertramp music video "Brother Where You Bound". He appeared in the Wing Commander franchise as Jacob "Hawk" Manley. He costarred with John Jenkins and Karen Landry in the 1988 indie film Patti Rocks. He appeared in the science fiction action film The Hidden, and the 1989 sci-fi cop film K-9000. He has appeared in more recent films as The Purge, Slow Burn, Sanitarium and The Identical. In 2014, he had a cameo role in Whiplash.
Mulkey played the supporting role of husband to Annie Potts's character in Any Day Now from 1998-2002. He has also appeared in Captain Phillips, Against the Wall, Cloverfield, the NBC TV movie Knight Rider, and 24, Boardwalk Empire, Friday Night Lights, Boomtown, Justified, Baretta and Twin Peaks.