Cullman graduated from Brown University in 1999, receiving a degree in Urban Studies and Visual Arts.

Cullman was a producer and director of photography on The House I Live In, which was the Documentary Grand Jury Prize winner at Sundance 2012 and was the recipient of the "React to Film" Award at Silverdocs.

On January 24, 2012, Cullman and Marshall Curry were nominated for an Academy Award for Best Documentary Feature for the film If a Tree Falls: A Story of the Earth Liberation Front.

In 2012, Cullman and Benjamin Rosen made Black Cherokee, a short subject, premiering in November 2012 as part of DOC NYC, a documentary film festival.

Cullman directed ReMastered: The Lion's Share which won the 2020 Emmy for Outstanding Arts and Culture Documentary.