Born in Toomevara, County Tipperary, Hassett first played competitive hurling during his schooling at the Patrician College, Ballyfin. He arrived on the inter-county scene at the age of twenty-seven when he first linked up with the Tipperary senior team. He made his senior debut in the 1960 championship. Hassett went on to play a brief role for Tipperary during a golden age for the team, and won one All-Ireland medal, two Munster medals and one National Hurling League medal. An All-Ireland runner-up on one occasion, Hassett also captained the team to All-Ireland victory in 1961.