Kammala jumla mai zuwa: Beukeboom ya buga wasan hockey na matasa don Sault Ste. Marie Greyhounds (1982<unk>1985). Bayan da aka zaba a zagaye na farko (19th overall) na
1983 NHL Entry Draft ta Edmonton Oilers, ya taka leda a juniors na tsawon shekaru biyu kafin ya shiga Oilers. Yayinda yake wasa da Oilers, ya lashe kofunan Stanley guda uku, kuma an san shi a matsayin mai tsaron gida mai ƙarfi.