Born Mohinder Purba in Nairobi, Kenya, Roy is a 52-inch (132 centimetre) tall dwarf.

Because of his short stature, he has played a variety of unusual characters in his acting career. He has played apes in two movies: Greystoke - The Legend of Tarzan, Lord of the Apes and again in the 2001 remake of Planet of the Apes (Two roles: One as a young gorilla boy and as the senator's daughter). His most noticeable (and notable) role is playing the Oompa-Loompas in Tim Burton's 2005 adaptation of Charlie and the Chocolate Factory. Deep had extensive training for the role in dance, yoga, and even some minor instrument playing.

He also had a cameo role in The Haunted Mansion (film), Corpse Bride (another Tim Burton movie), supplying General Bonesapart's voice. Another notable role was as the "pig-brained Peking Homonculus" or "Mr. Sin", a villain with a distinct appetite for homicide, in the acclaimed Doctor Who story The Talons of Weng-Chiang.

Deep Roy has also appeared in The X-Files, Blake's 7, Flash Gordon, Return To Oz, Big Fish, The NeverEnding Story, as the rider of the "racing snail" (credited as "Teeny Weeny") and Return of the Jedi, as a member of the Max Rebo band.

Deep can sometimes be confused with fellow Kenyan actor Kiran Shah.