Recruited from Swan Districts in the WAFL, Beasley moved to Melbourne in 1982 to pursue his career as a stockbroker, and signed with Footscray in the VFL. He made his debut in the Round 1 of the 1982 VFL season against a rampant Essendon side at Windy Hill, the Bulldogs losing heavily by 109 points. However, Beasley did not take long to establish himself as a prominent full-forward, kicking 12 goals against Geelong in Round 16 and ending his debut season with a very respectable 82 goals in an under-performing side.
In 1985, the Bulldogs rose up the ladder, finishing in second place at the end of the home-and-away season before losing to Hawthorn in the Preliminary Final. Beasley played a key role, taking out the Coleman Medal with 93 goals during the home-and-away season, his personal best. He reached the century mark with a seven-goal performance in the First Semi-final against North Melbourne and ended the season with 105 goals, becoming only the second Bulldog after Kelvin Templeton to kick 100 goals in a season. In 1988, Beasley kicked 82 goals to overtake Templeton as the Bulldogs' leading goalkicker, and retired from football in 1989 due to knee and back injuries.
Beasley obtained his bookmaker license in 2002. In 2009, he was charged with and pleaded guilty to breaching betting regulations between April 2006 and October 2008. Specifically, he had taken 1,598 bets totalling $3.8 million in turnover without lodging them with racing authorities. Beaseley was fined AUD$50,000 and disqualified from bookmaking for four years.