He was born in Astoria, Long Island on September 9, 1929 and was a son of the late Thomas and Nancy (Giaimo) Giangrasso. The family moved to Bridgeport, Connecticut in the early thirties and to Trumbull in 1938. He attended grammar school in Long Hill Trumbull and then later Central High in Bridgeport.
In 1948, he graduated from Williston Academy in Easthampton, Massachusetts. Following prep school, Dr. Giangrasso attended Georgetown University and later Fairfield University where he received his B. S. degree with Cum Laude honors in 1953. The following year, Dr. Giangrasso received an assistantship in biology at Boston College. In 1954, he was accepted into Creighton School of Medicine in Omaha, Nebraska where he received his medical doctorate in 1958.