Born in 1939 to a family with Jewish roots, Mednick attended Brooklyn College and became involved with New York's off-off-Broadway company Theatre Genesis, where much of his early work was staged.

In his teachings at Padua, Mednick stressed a strong grounding in theater and literary history, specifically the Ancient Greeks, Shakespeare, and Beckett.

[2] Padua ceased operation in 1995 and reemerged in 2001, premiering three Mednick works as part of a tribute series honoring influential local playwrights.

[4] Mednick's current productions include Mayakovsky and Stalin,[5] which premiered in Los Angeles starting in October 2018, and will move to the Cherry Lane Theatre in New York, 2019.

Past productions include; Scar (starring actor Ed Harris), an autobiographical series 16 Routines, Joe and Betty (concerning his parents' difficult marriage, starring John Diehl and Annabel Gurwitch, which performed in New York starting in June 2002), and Mrs. Feuerstein, [6] as well as Sand, The Hawk, Fedunn (produced by the Audrey Skirball-Kenis theatre), The Coyote Cycle, a series of one-act plays performed outdoors from twilight till dawn, involving four characters such as Spider Grandmother drawn from traditional Native American folklore.