Following shakedown in the Puget Sound area, Snook departed San Diego, California, on 23 June 1962 to deploy as a unit of the Seventh Fleet in the western Pacific, returning home on 21 December.

After returning to San Diego, Snook spent the next six months undergoing sound trials and drydocking, and on 16 April 1966, headed for the western Pacific.

Operating locally in the San Diego area through the first four months of 1972, Snook got underway on 13 May for a two-month tour supporting United States forces in Vietnam and visiting Kaohsiung, Taiwan.

She returned to San Diego on 16 June and began a four-week, postdeployment leave and upkeep period, followed by another four weeks engaged in sonar evaluation tests.

Snook was decommissioned and stricken from the Naval Vessel Register on 14 November 1986, and entered the nuclear-powered Ship and Submarine Recycling Program in Bremerton, Washington, and was scrapped between 1 October 1996 and 30 June 1997.