Cassidy won an appointment to the United States Military Academy at West Point. He graduated in 1931, after which he attended the University of Iowa, where he received a MS degree in Mechanics and Hydraulics.
After graduation he was commissioned in the United States Army Corps of Engineers. He served as assistant to the District Engineer in Portland, Oregon; commanded an engineer company at Fort Belvoir, Virginia; and oversaw military construction projects in Hawaii.
During World War II Cassidy commanded engineer troops specializing in airfield construction in England, North Africa, and Italy. He was Deputy Chief, then Chief, War Plans (later Operations and Training) Division, Office of the Chief of Engineers, in 1944-47.
At the outbreak of the Korean War, he was ordered to Japan where he was responsible for engineer supply. He served as South Pacific Division Engineer from 1955 to 1958 and was the senior logistics advisor to the Republic of Korea Army in 1958-59. Cassidy was the Corps’ Director of Civil Works from September 1959 to March 1962 and was then appointed Deputy Chief of Engineers.
On March 1, 1963, he became the Commanding General of the Army Engineer Center and Fort Belvoir and Commandant of the Army Engineer School. Cassidy became Chief of Engineers on July 1, 1965.