Small in stature, he mainly played as a rover and a forward. He is the grandson of Collingwood premiership player Jack Beveridge.
Beveridge won the Melbourne first year player award in 1989 and played his most games with the club in 1991.
He was traded to Footscray for pick 122 in the 1992 AFL Draft. He was seen as a depth player for the club's playing list. He managed 31 games in three seasons.
At the end of 1995 Beveridge was traded to St Kilda for pick 52 in the 1995 AFL Draft. His father was a recruitment officer for the club. Beveridge played 45 games for the Saints in four seasons. Beveridge played in St Kilda's 1996 pre-season cup winning side. He played in 7 of 22 matches in the 1997 home and away rounds. St Kilda qualified in first position for the 1997 finals series. He retired at the end on the 1999 season.
In 2002 Beveridge was elected in the AFL Greek Team of the Century for players having full or partial Greek heritage. His maternal grandfather originates from the island of Samos.
He began his coaching career in the Victorian Amateur Football Association competition where he coached St Bede's Mentone Tigers to the C, B and A Grade premierships in consecutive seasons.
Beveridge had two years as a player development manager at Collingwood from 2009–10, where he had an input to the club's 2010 premiership.
After having a year off, Beveridge joined Hawthorn in 2012 as an assistant coach specialising in working with the club's defence. Beveridge left Hawthorn after the 2014 season and was originally going to become director of coaching at St Kilda, however, on 14 November 2014, it was instead announced that he would become the head coach of the Western Bulldogs, succeeding Brendan McCartney.
Despite being tipped by many for the wooden spoon following the loss of several key decision makers including previous coach Brendan McCartney, captain Ryan Griffen, CEO Simon Garlick, former Brownlow Medallist Adam Cooney and over 700 games of experience at the end of 2014, as well as losing reigning best and fairest Tom Liberatore to a knee injury during the pre-season that would ultimately sideline him for the entire 2015 season, Beveridge led an impressive resurgence by the Western Bulldogs, which finished in sixth place on the ladder, and hence qualified for their first finals series since 2010, before losing to the Adelaide Crows in the elimination final at the Melbourne Cricket Ground. For his efforts, Beveridge was named the AFL Coaches Association coach of the year.
The following year, Beveridge led his team, the Western Bulldogs, to a victory in their first Grand Final since 1961 despite them suffering long-term injuries throughout the season, notably captain Robert Murphy. The Bulldogs had finished 7th in the minor premiership. They played in 3 consecutive elimination finals, two of them interstate. On the path to the grand final, they beat West Coast Eagles at Domain Stadium, Hawthorn at the MCG and Greater Western Sydney at Spotless Stadium. In an emotional display which, according to The Age, "will undoubtedly go down as one of the great moments in Australian sporting history", Beveridge handed his premiership medal to Murphy, saying, "This is yours, mate. You deserve it more than anyone". Murphy, though thankful, returned the medal the following day. It has since been placed in the Western Bulldogs museum. Later that month, Beveridge won the Spirit of Sport award at the Sport Australia Hall of Fame Awards for his gesture to Murphy. He was also named the AFL Coaches Association coach of the year for the second year running.Statistics are correct to the end of 2016
Harold Ball Memorial Trophy: 1989
AFL premiership coach: 2016
Jock McHale Medal: 2016
2× AFL CA Coach of the year: 2015, 2016
Spirit of Sport Award: 2016