Groves was born to William A. Groves and Ruth A. Flowers. Groves was hired in 1939 as a Bindery Assistant.
In April 1942, he was called into war service and was assigned to an X-Ray field unit. After the war, around October 1945, he returned to the Folger and applied his new skills in photography as a Photoduplication Assistant. He was later promoted to Head of Photoduplication and had a title change after that to Director of Photography.
While at the Folger, he met his future wife, Millie Lou Linton, whom he married on February 1, 1947. They had a son named Timothy William Groves (born July 27, 1949). She lived in Bethesda, Maryland from at least the 1970s until his death in 2001.