Severance was born in Houston, Texas, the daughter of Martha and John C. Severance. Her father was an IBM Systems Manager who had to move frequently around the world. According to Severance, "by the time I was 11, we'd lived in 12 different places." Severance and her family also lived in Libya, but in 1967 had to flee the country because of the Six-Day War. The family left the Middle East to return to the United States, and settled in Houston, Texas.
Severance attended Westbury High School and, at age 15, started modeling to make money for college. Although she hoped to become a veterinarian, she could not afford the cost of tuition. After appearing in the "Miss Houston" beauty contest, she was discovered by Alan Martin, a local photographer in Houston who introduced her to John Casablancas. Casablancas signed her up with the Elite modeling agency and sent her on assignment to Paris. During this time she met her future husband, model Eric Milan.
During her time in Paris, she posed for Sportswear International, Vogue Paris, and others. Upon her return to the United States, Severance became one of America's top models, filming over 40 commercials, and earning $7,500 per day.
Severance was also on the covers of the January 1990 and November 1992 issues of Playboy magazine, both featuring her in a nude pictorial. More recently, Joan, at age 52, appeared in a six-page editorial along with an interview in the Spring/Summer 2011 issue of Genlux Magazine.
In 1986, Severance began auditioning for acting bits at the urging of her friend Robin Leach. She made her debut in a small role in the first Lethal Weapon film in 1987. She usually takes the femme fatale roles in lower budget horror and murder-mystery movies, most notably Lake Consequence (1993), Criminal Passion (1994) and Payback (1995). She was featured alongside Richard Pryor and Gene Wilder in the 1989 comedy See No Evil, Hear No Evil, and as Hulk Hogan's love interest, Samantha N. Moore, in the wrestling film No Holds Barred (1989). She had leading roles in Roger Corman's Black Scorpion (1995) (she later starred in and co-produced a sequel, Black Scorpion II: Aftershock (1997)), and The Last Seduction II (1999).
Her most notable role is as a villainess on the TV series Wiseguy, where she played half of a brother/sister crime team (the other half was played by Kevin Spacey) to great acclaim. Their partnership was reprised in See No Evil, Hear No Evil. In the early 1990s, Severance appeared as Samantha "Sam" Dooley, the Martian Belle, in two training videos for Virtual World Entertainment alongside other actors such as Cheech Marin, "Weird Al" Yankovic, R. Lee Ermey, and Judge Reinhold.
Severance has appeared in the 2006 My Network TV telenovela Wicked Wicked Games, and in shows like CSI: Miami, One Tree Hill, and, in 2013, American Horror Story: Asylum.
She has also appeared in several music videos, including the Scorpions' video for the song, "Rhythm of Love".
Severance married fellow model Eric Milan in 1977. They separated amicably in 1984. According to Severance they "just grew apart".