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Millen was born in Kingston, Ontario. As a child he aspired to play in the National Hockey League until, at the age of 17, a friend offered him a part in a small play and he decided to pursue the performing arts instead. In secondary school at Queen Elizabeth Collegiate and Vocational Institute, he spent his Ontario Academic Credit year studying theatre. He subsequently attended Ryerson University's Theatre School and graduated in 2007 with a Bachelor of Fine Arts.
Millen signed with a talent agency in his fourth year of university, and one of his first roles was in a 2008 episode of the television series ReGenesis. In September 2008 he appeared in a Halifax production of Vern Thiessen's play Vimy, and in December 2008 he was cast in The Veil, a play written by Shahin Sayadi. The Veil opened in Halifax before relocating to Iran in January 2009, where the play was featured in Tehran's Fajr International Theater Festival.
From 2010 to 2013, Millen appeared in a variety of small roles in the television series Nikita, Rookie Blue, and State of Syn, as well as the horror films Monster Brawl and Exit Humanity. In August 2013 he successfully auditioned for a role on the second season of the science fiction series Orphan Black, after two unsuccessful auditions during the show's first season. It was announced in October 2013 that he had won the role of Mark. He spent six months filming Orphan Black 's second season, which aired in 2014, and returned for the third season in 2015.