Leupp is a native of City Island, New York. He is a 1983 graduate of Cardinal Spellman High School and studied theatre at Adelphi University. Calling himself "a gay guy who was never going to be passing for straight," he said that he had just started college when homophobic slurs were directed at him. “Here we go again, I thought; I was so used to it, in high school. But by the end of those four years, I had become very popular, by just being myself, and being relatable."

Leupp's first one-person show was Miss Coco Peru in My Goddamn Cabaret in 1992. Several more Coco Peru shows followed, as well as a 1994 guest role on New York Undercover and appearances in both Wigstock: The Movie and To Wong Foo Thanks for Everything, Julie Newmar in 1995. Peru next had a role in the 1997 romantic comedy Nick and Jane. Her follow-up was the 1999 independent film Trick. According to Peru, Trick Director Jim Fall was a friend and fan, and five years before the film was shot she helped him audition actors by reading the role which ultimately went to Tori Spelling. Peru's role in the film was added specifically for her: "They wrote me a part, which I rewrote using my own experiences. I wrote that line 'It burns.' Most of the part was written by me, which is why I played it so well."

Leupp knew he was gay at an early age. He met his husband Rafael Arias, a college professor originally from Spain, around 1995. In 2008 they married in Spain, where same-sex marriage is legal.

Peru later starred in Richard Day's Girls Will Be Girls (2003) and was one of six performers featured in the Logo original stand-up comedy series Wisecrack (2005). She has appeared in a number of other supporting and guest-starring roles in television and film, including Will & Grace in 2001, Arrested Development in 2005 and Twins in 2006; the Bravo reality series Boy Meets Boy (2003) and Welcome to the Parker (2007); the police procedural drama series Detroit 1-8-7 in 2011; the 2004 comedy film Straight-Jacket; and a 2007–2008 web series follow-up to Girls Will Be Girls. Peru performed the voice of "Mama Hippo" in the 2006 Disney animated feature The Wild, and later was the voice of Mother Morally Superior in a 2008 episode of the Logo stop motion animated series Rick & Steve: The Happiest Gay Couple in All the World. In 2004 Peru appeared in an Orbitz TV commercial that was later nominated for a GLAAD Media Award.

Since 2005 Peru has appeared in the "Conversations with Coco" series of live Celebrity interviews, most of which have taken place at the Renberg Theater at the Los Angeles LGBT Center. The events feature multimedia presentations of the guests' career highlights combined with a conversational interview by Peru. In 2012 Peru said that she started doing "Conversations" after being interviewed herself; with the host departing, the Center asked if she would like to continue the series. She agreed, inviting her friend Bea Arthur as her first guest. Peru's 2014 interview with Liza Minnelli raised $45,000 for the LA Gay & Lesbian Center.

In a 2008 interview, Leupp said that when Showtime passed on the Girls Will Be Girls concept as a situation comedy, it was instead produced as a film "hoping that the new gay networks would be interested." They were not, about which Leupp commented, "I think that drag is scary, even in our own community. They would rather play it safe. People want to be really politically correct, which I think is very dangerous. I’ve heard from various people in the Business that these stations are appealing to Middle America, and I find that very disturbing because I always felt that we as gay people were the Leaders — we decided what was funny, what was hot in fashion. Now we are trying to figure out what Middle America accepts. I’m not interested in that. I’m not trying to appeal to Middle America, and that gay people are doing so only makes me angry."

When asked what he was most proud of among Peru's many awards and recognitions, Leupp as Peru said in 2010, "I love when I get feedback from young gay people who tell me that my show or appearances on Logo helped them in a positive way to deal with their own identity. Recently, a young guy came up to me in Provincetown after my show and said, 'I love your anger. We’re not angry enough and you inspired me.' I was in heaven!"

Leupp stated in an October 2012 interview that as a young gay man he "decided to do drag as a way to express myself both in theater and as an Activist." "With friends who were sick, and dying of HIV/AIDS," he said in 2008, "I wanted to be an Activist as well as an entertainer.”

In November 2013, Leupp made headlines when he publicly protested the booking of a retired priest involved in reparative therapy to speak at Leupp's former high school, Cardinal Spellman Catholic in the Bronx. According to the school, Father Donald Timone would speak to parents about Catholic groups intended to convince children "struggling with same-sex attraction" to live "chaste lives through participation in support groups." Leupp said of the programs, "It makes it look like it’s a support group, but once you really see what they are doing it’s disturbing ... They are trying to shame these kids!" After further controversy over the issue among the school, alumni, gay Activists and anti-gay Activists, Timone's appearance was postponed until further notice but not officially cancelled.

"So I put all those things together: I’m a drag queen/two spirit/gay activist/entertainer. And everything fell into place. It was really a magical time in my life," Leupp said. To find Coco's signature hairdo, he tried blonde and black wigs but thought they looked terrible; when he tried red, Leupp said "that’s the color." "My first hairdo was very Tina Louise/Gilligan's Island — very big. It evolved into the straight with flip going under, then I tried it with the flip going out — and I said, ’That’s Coco.’ Other drag queens have chided me for not changing my hairdo, but I just feel it is so much part of the persona and so recognizable, I don’t want to change it." Leupp said his parents were very supportive, "But when I did do drag for the first time I had already done a one-person show about being gay. When I did that they were terrified — they thought I was going to have things thrown at me. But when I got applause, they realized there’s a big world out there that they didn’t know about. So when I decided to do drag, they were nervous, but hid it. And I think they were happy that I was received with such love when they expected me to be greeted with tomatoes."