Grasett was the third son of the Reverend Henry James Grasett, the Rector of St. James Cathedral in Toronto, and Sarah Maria Stewart. He was educated at a Toronto private school and at Leamington College for Boys in England. At 19, he returned to Canada and joined the Canadian militia. He fought on the Niagara Peninsula during the Fenian raid of 1866 with the 2nd Battalion, Volunteer Militia Rifles of Toronto, In 1867, he joined the British Army serving with The Royal Canadian Regiment in Canada and England and rose to the rank of lieutenant by the time he retired to Toronto in 1875, where he became a partner in a firm of shipping and commission merchants. In 1885, he was given the rank of lieutenant colonel in the militia and put in command of the 10th Battalion Royal Grenadiers which fought in several battles during the North-West Rebellion of 1885.