Copeland was born in Tacoma, Washington. Enlisted in the Naval Reserve in 1929, he was commissioned as a Naval Reserve officer in 1935. Copeland practiced law from 1935 until 1940, when he was ordered to active duty during the Navy's pre-World War II expansion. During the war, he commanded Pawtucket (YT-7), Black Douglas (PYc-45), Wyman (DE-38) and Samuel B. Roberts (DE-413).
During the Battle off Samar, 25 October 1944, while commanding Samuel B. Roberts, Lieutenant Commander Copeland led his ship and crew in an attack on superior Japanese battleship and cruiser force. Though his ship was lost, this action helped defeat the Japanese counter-offensive against the Leyte invasion. For this, he was awarded the Navy Cross.
Following World War II, Copeland resumed his law career while remaining a member of the Naval Reserve, in which he rose to the rank of Rear Admiral. Robert W. Copeland died at Tacoma, Washington, on 25 August 1973.
USS Copeland (FFG-25) was named for him.