Mamet was born in Randolph, Vermont. She is the daughter of American playwright, essayist, screenwriter, and film director David Mamet and actress Lindsay Crouse. Her maternal grandfather was playwright Russel Crouse, and her maternal great-grandfather was educator John Erskine. She has a sister, Willa, who is a singer, and two half-siblings, Clara, who is also an actress and director, and Noah. She lived in New England until age five when her mother moved to Pacific Palisades, California with Willa and Zosia. After finishing high school, Mamet decided to pursue acting instead of going to college.
Mamet has a band called Chacha.
In May 2013, Mamet and her sister Clara, dubbing themselves The Cabin Sisters, listed a project on the crowdfunding site Kickstarter, requesting $32,000 for a video of their song "Bleak Love", but the project only reached 6% funding after two days and less than $3,000 after 11 days.
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