Beardsmore began his career with Manchester United. He made his debut in September 1988 against West Ham United and was one of the first wave of "Fergie's Fledglings" to emerge. In only his second league start on New Year's Day 1989, he inspired Manchester United to a 3-1 home win over bitter rivals Liverpool at Old Trafford in the league, scoring one goal (his first for the senior team) and helping set up two others for Brian McClair and Mark Hughes.
He became a regular in the team for the rest of the 1988-89 season following the transfer of Gordon Strachan to Leeds United in March.
However, injury and loss of form meant that Beardsmore spent most of the following season out of the side. His first team chances were also limited by the arrival of Paul Ince and Neil Webb, while competition was also arising from the emergence of teenagers Lee Sharpe and Ryan Giggs.
Beardsmore was not selected in the squad for United's FA Cup triumph in 1990, the European Cup Winners' Cup triumph in 1991 (nor the Football League Cup final defeat that season), or the 1992 League Cup triumph. He played his final game for United in the 1991-92 season, during which he was loaned to Blackburn Rovers.
He collected the only senior medal of his career on 19 November 1991, when he was selected as a non playing substitute in United's 1-0 European Super Cup win over Red Star Belgrade at Old Trafford.
He did not feature in a single competitive game when United won the first Premier League title in 1992-93, and at the end of the season signed for Bournemouth on a free transfer. He remained at Dean Court until his retirement from playing in 1998, after five years at a club where he found some much-wanted regular first team action, though at a much lower level than he had been playing before (Bournemouth were members of Division Two in all five seasons that Beardsmore played for them).
Beardsmore also played five times for the England U-21 team in the late 1980s.
On 21 May 2008 while celebrating Manchester United's Champions League victory, Beardsmore was seen by police driving along Wessex Way, Bournemouth at excessive speed in a Land Rover. When stopped, Beardsmore was arrested for driving under the influence of alcohol. After a court appearance, he was banned from driving for 16 months and fined £300.
Beardsmore is currently employed by Bournemouth as a coach, having previously been the Assistant Community Officer at Bolton Wanderers during their early days in the Premier League.