He is best known for his role as medical examiner Sid Hammerback on the police procedural series CSI: NY, and his appearances in the films Atlantic City (1980), Ragtime (1981), Desperately Seeking Susan (1985), Land of the Dead (2005), and The Hills Have Eyes (2006).

[4] Joy played Madonna's punk musician boyfriend Jim in 1985's Desperately Seeking Susan, and the Dutch-Israeli Hans in the 1986 Alliance/CTV production Sword of Gideon, an adaptation of George Jonas's book Vengeance.

In 1998, he appeared in Gregory Hoblit's thriller Fallen, where he fit into the all-star cast that included Denzel Washington, Donald Sutherland, James Gandolfini, and John Goodman.

Joy stated, "I basically read the script and then look up everything on Wikipedia that I don't know, and try to find out how to pronounce all the long words and get my head around actually what it is that I'm conveying, because often my character has a lot of explaining to do.

In addition to his acting, Joy was frequently associated with the Newfoundland-based CODCO, working with the comedy troupe on many of their pre-television stage shows and appearing as a guest performer in the series.