Demme was born on February 22, 1944 in Baldwin, New York, the son of Dorothy Louise (née Rogers) and Robert Eugene Demme, a public relations executive. He graduated from Southwest Miami High School and the University of Florida.

Demme broke into feature film working for exploitation film Producer Roger Corman early in his career, co-writing and producing Angels Hard as They Come (1971), a motorcycle movie very loosely based on Rashomon, and The Hot Box (1972). He then moved on to directing three films for Corman's studio New World Pictures: Caged Heat (1974), Crazy Mama (1975), and Fighting Mad (1976). After Fighting Mad, Demme directed the comedy film Handle with Care (originally titled Citizens Band, 1977) for Paramount Pictures. The film was well received by critics, but received little promotion, and performed poorly at the box office.

Demme's next film, Melvin and Howard (1980), did not get a wide release, but received a groundswell of critical acclaim, and led to the signing of Demme to direct the Goldie Hawn and Kurt Russell star vehicle Swing Shift (1984). Intended as a prestige picture for Warner Bros. as well as a major commercial vehicle for Demme, it instead became a troubled production due to the conflicting visions of Demme and star Hawn. Demme ended up renouncing the finished product, and when the film was released in May 1984, it was generally panned by critics and neglected by moviegoers. After Swing Shift, Demme stepped back from Hollywood to make the Talking Heads concert film Stop Making Sense (also 1984) which won the National Society of Film Critics Award for best documentary; the eclectic screwball action-romantic comedy Something Wild (1986); a film-version of the stage production Swimming to Cambodia (1987), by monologist Spalding Gray; and the New York Mafia-by-way-of Downtown comedy Married to the Mob.

Demme was involved in various political projects. In 1981, he directed a series of commercials for the liberal advocacy group People for the American Way. The spots, titled "Eggs", "Music", and "Sports", were produced by Norman Lear and featured Muhammad Ali, Carol Burnett, and Goldie Hawn celebrating Freedom of Expression. In 1985, he directed a video for Artists United Against Apartheid. The short, featured various international Musicians including Afrika Bambaataa, Rubén Blades, Jimmy Cliff, Herbie Hancock, Little Steven, Run–D.M.C., and Bruce Springsteen, calling for a boycott of the South African luxury resort Sun City during Apartheid. His documentary Haiti Dreams of Democracy (1988) captured Haiti's era of democratic rebuilding after dictatorship, while his documentary The Agronomist (2008) profiled Haitian Journalist and human rights Activist Jean Dominique. Demme spent six years on the documentary I'm Carolyn Parker (2011), which highlighted rebuilding efforts in New Orleans Lower Ninth Ward after Hurricane Katrina.

Throughout 1986–2004, Demme was known for his dramatic close-ups in films. This style of close-ups involves the character looking directly into the camera during crucial moments, particularly in the "Quid pro quo" scene in Silence of the Lambs. According to Demme, this was done to put the viewer into the character's shoes. Beginning with Rachel Getting Married (2008), Demme adopted a documentary style of filmmaking.

Demme formed his production company, Clinica Estetico, with producers Edward Saxon and Peter Saraf in 1987. They were based out of New York City for fifteen years.

Demme directed music videos for artists such as Suburban Lawns, New Order, KRS-One's H.E.A.L. project and Bruce Springsteen. He also produced a compilation of Haitian music called Konbit: Burning Rhythms of Haiti that was released in 1989. (Lou Reed selected Konbit... as one of his 'picks of 1989').

Demme won the Academy Award for The Silence of the Lambs (1991)—one of only three films to win all the major categories (Best Picture, Best Director, Best Screenplay, Best Actor, and Best Actress). Inspired by his friend Juan Suárez Botas's illness with AIDS and fueled by his own moral convictions, Demme then used his influence to make Philadelphia (1993), one of the first major films to address the AIDS crisis and which garnered star Tom Hanks his first Best Actor Oscar. He also co-directed (with his nephew Ted) the music video for Bruce Springsteen's Best Song Oscar-winning "Streets of Philadelphia" from the film's Soundtrack.

Subsequently, his films included an adaptation of Toni Morrison's Beloved (1998), and remakes of two films from the 1960s: The Truth About Charlie (2002), based on Charade, that starred Mark Wahlberg in the Cary Grant role; and The Manchurian Candidate (2004), with Denzel Washington and Meryl Streep. Demme's documentary film Man from Plains (2007), a documentary about former U.S. President Jimmy Carter's promotional tour publicizing his book Palestine: Peace Not Apartheid, had its premiere at the Venice Film Festival and Toronto International Film Festival.

Demme was married twice, first to Evelyn Purcell and then Joanne Howard, with whom he had three children: Ramona, Brooklyn, and Jos. He was the uncle of film Director Ted Demme, who died in 2002. Demme's cousin was the Rev. Robert Wilkinson Castle Jr., an Episcopal priest who appeared in some of Demme's films.

His art-house hit Rachel Getting Married (2008) was compared by many critics to Demme's films of the late 1970s and 1980s. It was included in many 2008 "best of" lists, and received numerous awards and nominations, including an Academy Award nomination for Best Actress by lead Anne Hathaway. In 2010, Demme made his first foray into theater, directing Family Week, a play by Beth Henley. The play was produced by MCC Theater and co-starred Rose Marie DeWitt and Kathleen Chalfant.

Demme was a member of the steering committee of the Friends of the Apollo Theater, Oberlin, Ohio, along with Danny DeVito and Rhea Perlman. In 2013, he returned to Oberlin as part of an alumni reunion during the class of 2013 graduation ceremony and received the award for Honorary Doctor of Fine Arts.

Demme was an avid collector and devotee of Haitian art; in particular of Hector Hyppolite; so much so that he called it "an addiction". In 2014, he held an auction in Philadelphia selling thousands from his collection, much of which was donated to a cultural center in Port-au-Prince.

He returned to the concert documentary format with Justin Timberlake + the Tennessee Kids (2016), which he described as a "performance film, but also a portrait of an Artist at a certain moment in the arc of his career", and his last project was a history of rock & roll for the Rock and Roll Hall of Fame compiled from footage from Hall of Fame induction ceremonies set to debut in summer 2017.

On the morning of April 26, 2017, Demme died at the age of 73 in Manhattan, New York due to complications from esophageal cancer and heart disease.