Demme was born in New York City, the son of Gail (née Kern) and Frederick Rogers Demme. He grew up in Rockville Centre, New York on Long Island and attended South Side Senior High School. He graduated from SUNY-Cortland in 1985. He was the nephew of film producer and director Jonathan Demme.
Demme's media career may have begun with a radio show at WSUC-FM (SUNY-Cortland), a mix of comedy and talk radio with the usual sidekick, as well as some music and was widely listened to on and off campus. His career had modest beginnings—starting as a production assistant at MTV, he later became a producer in the On-Air Promotions Department and created the cable network's seminal hip-hop show Yo! MTV Raps (with Peter Dougherty), and directed other projects for them, including the infamous black-and-white rants starring then-unknown chain-smoking comedian Denis Leary.
Over the course of his career, he established a group of actors that he chose to work with on more than one occasion. The most frequently used of these was Leary, whom he directed as a lead or star in No Cure for Cancer, The Ref, and Monument Ave. Leary produced the 2001 crime drama film Blow, which starred Johnny Depp as George Jung and was directed by Demme.
Demme was married to Amanda Scheer, with whom he had two children. Scheer later opened several popular Los Angeles bars, including Teddy's at the Roosevelt Hotel, named in honor of her late husband. He was a fan of the Green Bay Packers.
On January 13, 2002, while playing a celebrity basketball game, Demme collapsed and died of a heart attack which may have been related to cocaine later found in his system during an autopsy. Actor Michael Rapaport was one of the participants in the game, and missed a taping of the IFC television series Dinner for Five, as discussed on season 1 episode 5 and season 1 episode 7 of that series. Demme was cremated, and his ashes were given to his family.
Much of one edition of the IFC program Dinner for Five was given over to a description of Demme's last night and fond reminiscences about his life, mostly by Denis Leary and the show's host Jon Favreau. This touched on Demme's being a fan of the Green Bay Packers and his fondness for playing practical jokes.
At the 2002 Golden Globe awards show, one week following Demme's death, Kevin Spacey wore a picture of Demme on his suit jacket. He was also in the 74th Academy Awards In Memoriam tribute that was also presented by Kevin Spacey.
His uncle Jonathan Demme's remake of Charade, The Truth About Charlie, was dedicated in his memory.
The 2003 album Blackberry Belle by The Twilight Singers led by Greg Dulli, was written in tribute to Demme, Dulli's close friend. Dulli had been working on another project, titled Amber Headlights (which would later see the light of day in 2005), but abandoned those sessions due to Demme's death. The recordings which followed, fueled in part by the memory of Demme, resulted in Blackberry Belle.
The 2002 film Punch-Drunk Love, written and directed by Paul Thomas Anderson, is dedicated to Demme.
Rock musician Greg Dulli wrote The Twilight Singers' 2003 album Blackberry Belle in Demme's memory.