His usual position is back row forward.
Groves played for Cardiff RFC, Glamorgan Wanderers RFC and Cross Keys RFC.

He made his debut for Newport Gwent Dragons against the Ospreys7 May 2010 as a second-half replacement. In the 2016–17 season, he joined Hong Kong Football Club (rugby section), playing in the Hong Kong Premiership.

He is a Wales Under 19 and Under 20 international. Groves captained the Wales Sevens team for the 2010 Commonwealth Games rugby sevens tournament.