Departing San Diego 3 April, she reported for one month's duty in the Formosa Patrol, during which time she participated in Operation Handclasp, carrying food, medicine, and clothing to the less fortunate people of free China.

Morton departed San Diego 31 October 1968, again joined the gun-line and bombarded North Vietnamese and Vietcong supply points and bunkers up and down the coast.

The destroyer returned home in the late spring and began preparations for an anti-submarine weapons system modernization at Long Beach Naval Shipyard.

As part of this refresher training, Morton conducted numerous ASW exercises against friendly submarines off Hawaii and California.

With the end of hostilities, Morton's ensuing deployments to WestPac centered around providing screen and escort services for carrier task forces.

During this cruise, the warship participated in ASW exercises off Taiwan and sailed into the Indian Ocean to visit Kenya and Iran, before returning home on 28 September.

Her name was struck from the Navy List on 7 February 1990 and the ship was sold to Southwest Recycling, Inc., Terminal Island, Calif., for scrapping on 17 March 1992.

During the scrapping process, the commercial diving crew responsible for removing the struts, shafts and wheels of the Morton set the current (as of 2007) world record for the thickest piece of steel cut underwater by means of an ultra-thermic torch.