Reznikov was born in Brooklyn on September 23, 1950. He first encountered The Living Theatre while a student at Yale in 1968. He joined the company in 1977, and became its co-artistic director along with Judith Malina following founder Julian Beck's death in 1985. Rezinikov and Malina were later married and continued to lead The Living Theatre, which currently operates out of its home at 21 Clinton Street in New York City.

He wrote and/or directed numerous productions for The Living Theatre, including Anarchia, And Then The Heavens closed, Body of God, Capital Changes, Clearing The Streets, Code Orange Cantata, A Dream Of Water, Enigma, and Utopia.

He is survived by his wife, Judith Malina.