Smigel began developing his comedic talent at The Players Workshop in Chicago, where he studied improvisation with Josephine Forsberg. Bob Odenkirk was a fellow student there. Smigel was also a member of the Chicago comedy troupe "All You Can Eat" in the early 1980s.

Smigel was born in New York City to Irwin Smigel and Lucia Smigel. He is Jewish and frequently went to Jewish summer camp. He attended Cornell University, studying pre-dental, and graduated from New York University in 1983 with a degree in political science.

Smigel first established himself as a Writer on Saturday Night Live by joining the writing staff when Lorne Michaels returned as executive Producer for the 1985–1986 season. Smigel was hired after then-SNL producers Al Franken and Tom Davis saw Smigel in a Chicago Sketch show. After the 1985–1986 season proved to be a disappointment with critics, in the ratings, and with Brandon Tartikoff (who was planning to have SNL canceled by the last episode of season 11 due to its sliding ratings), Michaels fired most of the cast and Writers, retained the cast and Writers who were standouts during the otherwise dismal season (Smigel being one of them), and hired new ones for the 1986–1987 season. This is when Smigel began to write more memorable sketches, including one where host william Shatner urged worshipful attendees at a Star Trek convention to "get a life." Smigel rarely appeared on screen, though he was credited as a featured player in the early 1990s and played a recurring character in the Bill Swerski's Superfans sketches.

While on a writers' strike from Saturday Night Live following the 1987–88 season, Smigel wrote for an improvisational comedy revue in Chicago with fellow SNL Writers Bob Odenkirk and Conan O'Brien called Happy Happy Good Show.

In 1996, Smigel wrote and performed on the short-lived Dana Carvey Show, a primetime Sketch comedy program on ABC. Despite its premature end, the show provided Smigel the opportunity to debut his first cartoon, The Ambiguously Gay Duo. Upon the show's cancellation, Smigel continued developing more cartoon ideas the following summer and would begin airing them on Saturday Night Live under the TV Funhouse banner. Smigel would later claim, "My whole career came out of the impulse to do cartoons on The Dana Carvey Show."

Smigel's most famous creation, however, would be the foul-mouthed puppet Triumph, the Insult Comic Dog, who mercilessly mocks celebrities and others in the style of a Borscht Belt Comedian. This character debuted on Late Night with Conan O'Brien in February 1997 and would continue to make appearances on the show, as well as others, for many years to come.

In 2000, he voiced a sage bulldog in Little Nicky. Smigel, along with Adam Sandler and Judd Apatow, wrote the script for the film You Don't Mess with the Zohan in which Smigel played Yosi, an Israeli electronics salesman. Smigel is also one of the executive producers of the film, which is a first for him despite his frequent collaborations with Sandler.

Smigel has a wife, Michelle, and three children. Michelle and Robert serve on the board of New York Collaborates for Autism due to their eldest child being autistic. They are active members of (NYCA), a non-profit organization founded in 2003 to address the needs of individuals and families who are living with autism. Smigel created the Night of too Many Stars, a biannual Celebrity fundraiser to benefit autism education. He won an Emmy on the 2012 broadcast of Night of Too Many Stars for his writing.

It was reported in 2006 that Smigel and Adam Sandler were working on an animated sitcom for Fox called Animals. Fox has not made any official statement regarding the show. Additionally, Smigel played a gay mailman in the Adam Sandler film I Now Pronounce You Chuck and Larry and Yari the Mechanic in the "Mister Softee" episode of Curb Your Enthusiasm.

Currently living in New York, he co-wrote and co-executive produced the films Hotel Transylvania (2012) and Hotel Transylvania 2 (2015), in which he voiced Marty, a fake version of Dracula, and Harry Three-Eye, respectively. In the fifth season of the FX show, Louie, Smigel received a story credit on the episode "Cop Story", as a similar incident as to what appears in the show actually happened to him, down to the cop crying in his apartment while Smigel went out, found the missing gun and carried it home, terrified that anyone would notice. Michael Rapaport's character wasn't based on the man Smigel knew, however, since all Smigel ever told Louis C.K. about was the gun itself.

Smigel created, wrote, executive produced, and starred as Triumph the Insult Comic Dog in The Jack and Triumph Show, alongside Jack McBrayer in 2015. It was announced in January 2016 that Smigel would be starring as Triumph in Triumph's Election Special 2016 on Hulu the following February.