Greaves began racing in buggies and won two championships before to Pro Light. He won seven Pro Light championship between SODA and its predecessor CORR. He raced one year in a Pro 2 Trophy Truck before moving into Pro 4, the premiere class in short-course off-road racing. Greaves won class championships in CORR in 2004 and 2006 as well as WSORR in 2007. After those sanctioning bodies dissolved, he won the 2010 Traxxas TORC Series champion in their Pro 4x4 division. He continued racing in the Pro 4 division, winning the 2013 title.