Graeme was born in Manchester. He competed in both the T36 100m and 200m in the 2004 Summer Paralympics in Athens winning the bronze medal in 200m. Four years later, he competed in the 100m, 200m and 400m but won the silver medal in the T36 100m in the 2012 Summer Paralympics. He has also competed for the national 7-a-side football team and competed at a national level in swimming. Graeme has the world record in T36 100m.
He won two silver medals at the 2014 IPC Athletics European Championships in the T36 100m and 200m in Swansea. He finished just ahead of his team mate Paul Blake in the 100m but on both occasions, the Briton was beaten to the gold medal by the Russian Evgenii Shvetcov. Ballard also reached the final of the 400m where he recorded a personal best of 57.18 to finish in fourth place. He placed fifth in the Rio Paralympic games with 12.84 seconds after a false start that disqualified another Ukrainian athlete and a new Paralympic record being set by a Malaysian athlete.