Beukeboom played junior hockey for the Sault Ste. Marie Greyhounds (1982–1985). After being selected in the first round (19th overall) of the 1983 NHL Entry Draft by the Edmonton Oilers, he played in juniors for two more years before joining the Oilers. While playing for the Oilers, he won three Stanley Cups, and was known as a hard-hitting defenceman.