The band grew out of a local band, Loud Fast Rules, that formed in 1981 with Dan Murphy, Dave Pirner, Karl Mueller and Pat Morley. Morley was later replaced by Grant Young in 1984. The band recorded three albums with Twin/Tone Records and two with A&M Records to little commercial success. However, in 1992, they released the double-platinum album Grave Dancers Union, featuring their Grammy Award-winning single "Runaway Train". The band played the Bill Clinton inauguration later that year. They also scored a platinum record with the album Let Your Dim Light Shine three years later, but it was the last hit album of the band's career. Mueller was diagnosed with cancer in 2004, causing the band to organize a benefit concert on his behalf, and passed away a year later. As of 2007, the band continues to perform live shows.
Their 1984 debut album, Say What You Will... Everything Can Happen was originally released on LP and cassette by local record label Twin/Tone as a 9 song EP. This is since out-of-print, but was re-released on CD as Say What You Will, Clarence...Karl Sold the Truck, which includes five additional tracks that were cut from the original album. Between the release of Say What You Will and their second album, Grant Young joined the group, taking over the drums from Morley. In 1986, Soul Asylum released three albums, Made To Be Broken followed by the cassette only release of Time's Incinerator and While You Were Out. Despite critical acclaim locally and internationally, they remained unknown to the larger US audience.
The group signed with A&M Records in 1988. Shortly after releasing their first record with A&M, one final album from Twin/Tone was released, and speculation remains that this album may have ruined their chances of success with A&M. The album was Clam Dip & Other Delights (1989), a parody of A&M Records co-founder Herb Alpert's Whipped Cream & Other Delights. According to legend, Alpert was less than delighted. The titles of the A&M albums may show the group's frustration. Hang Time was released in 1988, followed by And the Horse They Rode in On in 1990 (Produced by X-pensive Winos drummer Steve Jordan). Due to poor sales and Dave's hearing problems, the group considered disbanding.
After playing a series of acoustic shows in the early 1990s they were picked up by Columbia Records. In 1992 they released Grave Dancers Union, which became their most popular album. On January 20, 1993, the group performed at the first inauguration of United States President Bill Clinton. The next year, Soul Asylum received the Grammy Award for Best Rock Song for "Runaway Train." The music video for "Runaway Train" featured photographs and names of missing children in a public service video style. At the end of the video, Pirner appears and says "If you've seen one of these kids, or you are one of them, please call this number" before a missing children telephone helpline number appeared. For use outside the USA, the video was edited to include photos and names of missing children from the area the video would be used. The video was instrumental in reuniting several children with their families.
Before their next studio album, drummer Grant Young was fired, and was replaced by Sterling Campbell. Campbell had been listed as providing "percussion" on Grave Dancers Union (although it turned out he had actually done at least half of the drumming on that album ). The next release, Let Your Dim Light Shine saw the track "Misery" reach the Top 20, but the album was not as successful as the band's previous one. In 1997 Soul Asylum performed a benefit concert for North Dakota students whose proms were cancelled due to the Red River Flood of 1997. some of the songs that were played during the prom were later released on After the Flood: Live from the Grand Forks Prom, June 28, 1997 in 2004. The group released Candy from a Stranger the following year. The album was unsuccessful and the band was dropped from Columbia Records' roster. Pirner said, "It's sort of sad to say, but you could see the whole grunge-rock-band thing getting totally over-saturated and people were looking for something new." The band took a step back; Pirner explained, "We needed to reassess how far we've gone and how much further we're going to go and which way we want to go and what we do right and what we do wrong. It was kind of time to take inventory.
Dave Pirner has become good friends with director Kevin Smith, a longtime Soul Asylum fan. Soul Asylum have contributed music to three Kevin Smith films, Clerks, Clerks II, and 1997's Chasing Amy (in which Pirner provided the score). Smith directed the music video for the song "Can't Even Tell," which was featured on the Clerks soundtrack.
In May 2004, bassist Karl Mueller was diagnosed with throat cancer and underwent treatment. In October 2004, a benefit concert was held for him in Minneapolis at The Quest nightclub, and featured many popular local groups and musicians, including Soul Asylum, the Gear Daddies, Paul Westerberg, and former Hüsker Dü bandmates Bob Mould and Grant Hart, who reunited for their first performance together in sixteen years. The benefit raised over $50,000. At the time, Mueller's cancer was in remission, and he played with his bandmates during the show. Mueller recorded his last Soul Asylum album that year, 2006's The Silver Lining. However, the cancer later returned, and he died at his home on June 17, 2005. Soul Asylum released The Silver Lining on July 11, 2006, their first album of new material in eight years since Candy from a Stranger. The new album has been referred to as considerably more "old school" than Candy from a Stranger.
In late 2005, ex-Replacements bassist (and current Guns N' Roses bassist) Tommy Stinson and former Prince drummer Michael Bland joined Soul Asylum in tribute to the late Karl Mueller. They completed their American tour in support of The Silver Lining in late 2006. In November and December 2006 they opened for Cheap Trick on their American tour. On March 10th, 2007, Soul Asylum joined Cyndi Lauper, Mint Condition, and Lifehouse to hold a concert to benefit Wain McFarlane, the leader of the legendary reggae band Ipso Facto, to help pay for the expenses of a kidney transplant.