Tirry was born in County Cork, Ireland in 1608, the nephew of the bishop of Cork-Cloyne. He joined the Augustinian Order in Cork and studied in Valladolid, Spain and Paris, France. Upon completion of his education in Paris, he spent five years (1636–1641) in Brussels, Belgium.
He returned to Ireland in 1641, and in 1649 was chosen as Prior (local superior) of the Augustinian house in Skreen. This was the same year that marked the beginning of the Cromwellian conquest of Ireland. A law was enacted on January 6, 1653 declaring that any Roman Catholic priest in Ireland was guilty of treason. Tirry was forced into hiding alongside other priests, but was captured when three men reported his whereabouts for money.
William was imprisoned at Clonmel and refused to adopt the Protestant religion. He was executed by hanging on May 12, 1654. An account told by a friar who had been tried with William supplies some details of the day: "William, wearing his Augustinian habit, was led to the gallows praying the rosary. He blessed the crowd which had gathered, pardoned his betrayers and affirmed his faith. It was a moving moment for Catholics and Protestants alike."