Dizzia is the daughter of Lorraine (née Bladis) and John Paul Dizzia. She was raised in Cranford, New Jersey. She has a sister who is a Lawyer. She graduated from Kent Place School in 1993, receiving the Drama Award upon graduation. She studied theater at Cornell University. She received her Master of Fine Arts from the University of California, San Diego.
Dizzia performed the role of Eurydice in the Sarah Ruhl play Eurydice in regional theatre and Off-Broadway at the Second Stage Theatre, from June 18, 2007 to August 26, 2007. She performed in another Sarah Ruhl play In the Next Room on Broadway at the Lyceum Theatre, from October 22, 2009 to January 10, 2010. Her performance earned her a 2010 Tony Award nomination for Featured Actress in a Play.
Dizzia appeared in the premiere production of the Amy Herzog play Belleville at the Yale Repertory Theatre, from October 21, 2011 to November 12, 2011. She then appeared in the play Off-Broadway at the New York Theatre Workshop from March 3, 2013 to April 14, 2013. She was nominated for the 2013 Drama Desk Award, Outstanding Actress in a Play.
