Rubuta ci gaba don wannan sakin layi - An haifi Stevens a Brockton, Massachusetts, amma ya girma a Pembroke, Massachusetts. A lokacin da yake matashi, ya taka leda a gasar 1978 na Quebec International Pee-Wee Hockey tare da 'yan wasan hockey na Hobomock daga Pembroke. Yayin da yake halartar Makarantar Sakandaren Yankin Silver Lake a Kingston, Massachusetts, Kevin Stevens ya buga wasan hockey da baseball. An gayyace shi don gwadawa duka biyu na Toronto Blue Jays da Philadelphia Phillies; duk da haka, yarda cewa ba shi da babban hitter a baseball, sai ya yanke shawarar buga wasan hockey a maimakon haka. Stevens ya karɓi cikakken tallafin karatu don buga wasan hockey don Kwalejin Boston, kuma an tsara shi a zagaye na shida (108th gaba ɗaya) a cikin NHL na 1983
ta hannun Los Angeles Kings. Bayan watanni da yawa, an yi musayar haƙƙoƙinsa zuwa Pittsburgh Penguins don Anders Håkansson, mai tsaron ragar hagu daga Sweden wanda kwanan nan aka yi musayarsa zuwa Penguins tare da Ron Meighan daga Minnesota North Stars don zaɓar zagaye na farko na Penguins a cikin shirin 1983 (Brian Lawton).