Beukeboom played junior hockey for the Sault Ste. Marie Greyhounds. After being selected in the first round 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. Beukeboom was traded from the Edmonton Oilers to the New York Rangers on November 12, 1991. At the time, neither the Rangers nor Oilers made any announcement to indicate that Beukeboom was part of the Mark Messier trade. He is tall and heavy. He played on the top defensive pairing with Brian Leetch, and was an alternate captain. Beukeboom's stay-at-home play allowed Leetch to lead the rush and kept opposing players out of the goal crease. He led the team in penalty minutes three times and won his last Stanley Cup with the Rangers in 1994. He was also known for his philanthropy, including Ice Hockey in Harlem. Beukeboom won the Rangers' Crumb Bum Award, given for service to local youngsters, in 1996. While with the Rangers, Beukeboom also appeared in a memorable This is Sportscenter spot in which he assaults ESPN's Steve Levy after being told Levy had referred to Beukeboom as "Puke-a-boom." Due to his physical play, Beukeboom suffered multiple concussions, the most devastating of which came as a result of a sucker punch by Matt Johnson of the Los Angeles Kings in November 1998. Johnson received a 12-game suspension for intent to injure. While Beukeboom returned after a few games off, he bumped his head again in a minor collision with Martin Gelinas in February 1999 and he was forced to miss the rest of the season. Afterward, Beukeboom was left with recurrent headaches, memory loss, nausea, and mental fogginess that lasted for months. He was diagnosed with post-concussion syndrome, and ordered to never play hockey again. Beukeboom officially retired in July 1999 with a total of 1,890 NHL penalty minutes in 804 games played, and is currently second all-time on the Rangers' penalty minutes list. Even after retiring, he continued to suffer post-concussion symptoms for almost two years before recovering.
Beukeboom returned to hockey as an assistant coach for the Toronto RoadrunnersAmerican Hockey League for the 2003–04 season. In 2005, he became the president and part owner of the Lindsay Muskies of the Ontario Provincial Junior "A" Hockey League, and in 2008, Beukeboom became an assistant coach for the Barrie Colts of the Ontario Hockey League and worked in both teams. In June 2009, Beukeboom was named the assistant coach of the Sudbury Wolves of the Ontario Hockey League. That same year, he served as a coach for Team Canada Red at the World Jewish Hockey Tournament. In 2012, he returned to the AHL as an assistant coach for the Connecticut Whale who would later be renamed to Hartford Wolf Pack. On July 1, 2016, he was hired as an assistant coach for the New York Rangers.