As a boy, D'Amico played church hockey in Toronto, moving up to junior B and then realizing he could go no further. He got a job in construction, but a friend suggested he try officiating church hockey. He did, and he loved it. He was also good at it, and those in the game took notice. D'Amico moved up to the Toronto Hockey League and then the OHA, and in 1963 he worked on the line for an NHL exhibition game in Kitchener. At that point, NHL Referee-in-Chief Carl Voss offered him a pro contract because Ron Wicks had created an opening by moving up to a referee's position. D'Amico's first regular season game was on October 12, 1964, and when he retired in 1987 he was the last of the Original Six officials.
D'Amico spent part of one season as a referee (mostly in the Central League but 21 games in the NHL) but decided he was more comfortable on the lines, helping players rather than judging them. Over the years, he suffered his share of injuries. He broke his arm after taking a puck in one game, suffered a severe hamstring pull after sliding into the goal on another night, and once suffered a serious gash to his thigh after working in a pair of skates in his living room!
Perhaps more than any other official, D'Amico maintained a high profile in the off season, using his name and position to do countless hours of charity work both on his own and in conjunction with golf and tennis tournaments and other appearances by the players themselves.
D'Amico once rejected overtures from the WHA to join the pirate league as an official, and he went on to officiate in four Canada Cup tournaments as well as the Challenge Cup and Rendez-vous series that replaced the All-Star games in 1979 and '87 respectively. He also appeared in 20 Stanley Cup finals' series. During his last season, 1986-87, D'Amico worked a reduced schedule of 40 games, weaning himself off the love of his life and preparing for his second career, in the NHL's head offices in Toronto. The following year he joined the league's Officiating Supervisory staff, though his career was not yet fully over. On the night of March 5, 1988 he was at home watching the Leafs on TV when one of the linesmen was injured and had to leave. D'Amico packed his skates and headed down to Maple Leaf Gardens, working one last time on an emergency basis!