Roger Griswold attended Harvard University. For about eight months in 1916 he served with Section Sanitaire [Etats-] Unis (SSU) 2 of the American Field Service (AFS), a volunteer ambulance organization serving with the French Army in World War I. In late 1917 or 1918, after the United States entered the war and AFS ceased to exist as an independent organization, Griswold returned to war service as a Captain of the U.S. Field Artillery. After the war, he continued his association with AFS, becoming a vice president of the American Field Service Association. During his tenure, Griswold strove to increase membership of the AFS Association, which was formed between the World Wars as a veterans organization intended to continue the positive Franco-American relations they had fostered during the war.
Griswold married Penelope B. Parkman of Boston, and the couple had at least one child, Roger Griswold, Jr.