Stevens started playing young, achieving his first aged just 12. He turned professional aged 20, and reached the semi-finals of the World Championship aged 21. In 1984, he achieved a televised maximum 147 break in a match against Jimmy White in the Benson & Hedges Masters, which remained the only such break ever made in the competition until Ding Junhui achieved a 147 break in 2007. Ken Doherty and Stephen Hendry came close to repeating the feat. His stylish choice of attire and his youthful popstar good looks made him a ladies` favourite.
His career ran into problems in 1985 when he met South African Silvino Francisco in the Dulux British Open final. After Stevens lost 9–12, Francisco accused him of taking stimulants. Francisco was subsequently fined by the world snooker association for the comments. Kirk Stevens never failed a drug test in the entirety of his professional career but shortly after the comments were made public Stevens admitted to an addiction to cocaine. Although he underwent treatment, his career never really recovered. He dropped out of the top 16 in 1986/87, but continued to play on until 1992/93 before returning home to Canada and retiring from professional tournament play on the world circuit. He returned to the game and won a place on the professional tour again in 1998/99 but never qualified for the following season. He almost returned for the 2000/01 season but lost in the North American qualifying final to Bob Chaperon.
He continues to play snooker in various Canadian events, including charity events. He has won the Canadian Open Championship in 1997, 1998, 2000 and 2002 and also reached the semi-finals in 2005.