Born in Sallingsund, Graversen rode in Britain for Mildenhall Fen Tigers in the 2008 season after first riding at the track in 2007, ending the year as the club's top scorer. In 2009 he rode for King's Lynn Stars, the team winning the Premier League, Premier Trophy and Knock-out Cup that year. In 2010, with his CMA too high for King's Lynn to give him a place, he was loaned out to Redcar Bears, Stoke Potters, and Scunthorpe Scorpions, and won the Kenny Smith Memorial Trophy at Scunthorpe that year. He signed for Leicester Lions for 2011, finishing the season as the team's highest scorer and only ever-present rider. He has raced in Denmark for Slangerup.