D'Amico was born in Rochester, NY and was raised in Buffalo, NY. He began playing professionally with Paul Specht's band in 1936. That same year, he joined Red Norvo. In 1938, D'Amico began radio broadcasts with his own octet before returning briefly to Norvo's group in 1939. He played with Bob Crosby's orchestra in 1940 and 1941, then had his own big band for about a year. D'Amico had short stints in the bands of Les Brown, Benny Goodman and Norvo again before working for CBS in New York. He also found time to play with Miff Mole and Tommy Dorsey. D'Amico spent ten years as a staff musician for ABC, and then played with Jack Teagarden in 1954. From that point he mostly worked with small groups, infrequently forming his own band. D'Amico played at the 1964 World's Fair in New York with The Morey Feld trio.