Kaufman was born in New York City to a Jewish family on November 19, 1958, the son of Helen and Myron Kaufman. He grew up in Massapequa, New York before moving to West Hartford, Connecticut where he graduated high school. While attending high school, Kaufman was part of the school's drama club, performing in numerous productions before landing the lead role in a production of Play It Again, Sam during his senior year.

Kaufman lived and worked for a time during the late 1980s in Minneapolis, answering calls about missing newspapers at the Star Tribune, before moving to Los Angeles.

Between 1983 and 1984, Kaufman and Proch wrote comedic articles and spoofs on spec for National Lampoon. His work included parodies of Kurt Vonnegut and the X-Men. Kaufman and Proch tried to get their screenplays produced, sending them to many people in film industry. The only response the two ever received for their work was a supportive letter from Alan Arkin in regards to their screenplay titled Purely Coincidental. In hope of finding talent agents the two began to write spec scripts for television series such as Married... with Children and Newhart. In 1991, Kaufman moved from Minneapolis to Los Angeles in search of more job prospects. Kaufman got his start in television by writing two episodes for Chris Elliott's Get a Life during the 1991–1992 season. During the 1993–1994 season, Kaufman worked on Fox's Sketch comedy show The Edge. Kaufman wrote some pilot scripts while working as a television Writer, but none of them were produced. He later worked as a Writer for Ned and Stacey and The Dana Carvey Show.

He first came to mainstream notice as the Writer of Being John Malkovich, directed by Spike Jonze, earning an Academy Award nomination for his effort and winning a BAFTA. He wrote the script on spec in 1994, sending it to many companies and studios, all turning it down. The script eventually reached Francis Ford Coppola, who passed it on to his then-son-in-law Jonze, who agreed to direct the film.

Eternal Sunshine of the Spotless Mind, released in 2004, was Kaufman's second pairing with Director Michel Gondry. Kaufman won his first Academy Award for Best Original Screenplay and third BAFTA for the film together with Gondry and French Artist Pierre Bismuth. The trio also received the prestigious PEN American Center 2005 prize for screenplay for the film. David Edelstein described the film in Slate as "The Awful Truth turned inside-out by Philip K. Dick, with nods to Samuel Beckett, Chris Marker, John Guare—the greatest dramatists of our modern fractured consciousness. But the weave is pure Kaufman."

After agreeing to participate in Carter Burwell's Theater of the New Ear, a double bill "sound play", Kaufman wrote and directed the audio play Hope Leaves the Theater, while the other play in the production, titled Sawbones, was written and directed by the Coen Brothers Theater of the New Ear debuted in April 2005 at St. Ann's Warehouse in Brooklyn, New York. Due to scheduling conflicts, later productions of Theater of the New Ear did not feature the Coen's play, replacing it with Anomalisa which was written by Kaufman under the pseudonym "'Francis Fregoli".

Kaufman made his directorial film debut with the postmodern film Synecdoche, New York. It premiered at the Cannes Film Festival in 2008. The idea for the film came when Kaufman and Spike Jonze were approached to direct a horror film. Rather than make a conventional horror film, the two agreed to have the film deal with things they found frightening in real life, rather than typical horror film tropes. Kaufman decided to direct the film after Jonze left the project as the Director to direct Where the Wild Things Are instead.

Kaufman was slated to write and direct a film with the working title Frank or Francis. Few details have been confirmed about the plot except that it is a musical comedy about internet anger culture. In July 2012, Jack Black, who was to star in the film, revealed in an interview that funding for the project had fallen through, as the studio was unsure about its chances for success after the financial failure of Kaufman's last directorial effort. Although the Future of the project is not certain, Kaufman says "It could still happen. It would have to be reinvented, though. We had a whole cast and we were headed into pre-production. So, I’d have to get people back and who knows if they would be interested anymore. But, at this point, we don’t have any money, so that’s a secondary concern."

Trying to make a return to television, Kaufman directed and wrote a pilot for FX titled How and Why in 2014. The plot was described as being about a "man who can explain how and why a nuclear reactor works but is clueless about life". FX decided to not pick up the pilot, but it has been shopped to other outlets.

Dino Stamatopoulos, a former colleague of Kaufman's from The Dana Carvey Show, became interested in adapting Kaufman's Anomalisa play script into a stop motion animated film. With Kaufman's permission, Stamatopoulos turned to the crowdfunding website Kickstarter in order to fund the film. The Kickstarter page for the film was set up in August 2012 and by the time funding had ended $406,237 was pledged. It had its world premiere at the Telluride Film Festival on September 4, 2015, receiving universal acclaim from critics.

In May 2017, he was announced as one of the three Writers of the upcoming film adaptation of the Patrick Ness' Chaos Walking book series, together with John Lee Hancock and Ness himself.