Sanders was born on April 16, 1953 in Austin, Texas, to Phyllis Rae (née Aden) and James Olcutt Sanders. After attending the acting conservatory at SUNY Purchase, Sanders made his Off-Broadway debut in a Shakespeare in the Park production of Henry V in 1976. He played Bradley in the first New York production of Sam Shepard’s Buried Child in 1978.

Off-Broadway, he appeared as George W. Bush in Sir David Hare’s Stuff Happens in 2006. He then played in a number of Shakespearean plays: A Midsummer Night’s Dream (Bottom, 2007), Hamlet (Ghost of Hamlet’s Father/Player King/Gravedigger, 2008), Twelfth Night (as Sir Toby Belch, 2009), and the title role in Shakespeare’s Titus Andronicus (2011).

On television, Sanders played mob lawyer Steven Kordo in the 1986–88 NBC detective series Crime Story, Norbert “Ziggy” Walsh on two episodes of Roseanne, and recurring characters on shows such as Person of Interest and True Detective. He is the narrator for the PBS series Wide Angle from 2002–2009 and has served as narrator for a number of Nova episodes starting in 2007.

Sanders appeared in the Richard Nelson Apple Family Plays, a series of plays which ran Off-Broadway at the Public Theatre in 2010 (That Hopey Changey Thing), 2011 (Sweet and Sad), 2012 (Sorry), and 2013 (Regular Singing).

In 2015, Sanders debuted his first play, Unexplored Interior, about the Rwandan genocide, at the Atlas Performing Arts Center in Washington, D.C.