Smith grew up in Columbus, Ohio and graduated from Hilliard Darby High School in 2005. He had aspirations ranging from becoming a concert pianist to a lawyer. While at Otterbein University, he was cast in such plays as The Scene, The Caucasian Chalk Circle, Who’s Afraid of Virginia Woolf?, and Tartuffe. He majored in art musical theater and minored in jazz piano, although he considered dropping out of art musical theater for philosophy or pre-law.

In 2011, Smith was seen in the New York City premiere of The Shaggs: Philosophy of the World at Playwrights Horizons and in 2009 to early 2012 could be seen in various regional theatre productions for the likes of New York Stage and Film. He starred in The Fantasticks at both Barrington Stage Company and The Repertory Theatre of St. Louis. He was also seen in Edith Can Shoot Things and Hit Them.

Smith made his Broadway debut in Breakfast at Tiffany’s in 2013. In the same theatre season, he also starred Off-Broadway in both the U.S. premiere of Cock a.k.a. The Cockfight Play by Mike Bartlett and The Whale by Samuel D. Hunter which had its world premiere at Denver Center for the Performing Arts with the New York premiere at Playwrights Horizons. His first feature film was Camp X-Ray which premiered at the 2014 Sundance Film Festival in January. He appeared in a short horror movie, Dog Food, co-starring Amanda Seyfried and premiered at the 2014 South by Southwest in March. Smith also appeared in the HBO mini-series Olive Kitteridge and the film Carol. In 2018, he starred in his first leading role in the independent drama 1985.