Potter was born in Lapeer, Michigan and attended the public schools there. He received an AB degree from Eastern Michigan University, Ypsilanti, Michigan, in 1938. He worked as an administrator of Bureau of Social Aid in Cheboygan County, Michigan, 1938-1942. In 1942, he enlisted as a private in the United States Army with combat service in the European Theater of Operations with the US 28th Infantry Division. He was seriously wounded at Colmart, France, in 1945, resulting in the loss of both legs. He was discharged from the service as a major in 1946. He was awarded the Silver Star twice, the French Croix de Guerre, and the U.S. Purple Heart. After the war, he was engaged as a vocational rehabilitation representative for the Retraining and Reemployment Administration with the United States Labor Department until his resignation in 1947.

Potter was elected on August 26, 1947, as a Republican to the United States House of Representatives from Michigan's Eleventh District for the Eightieth Congress to fill the vacancy caused by the death of Frederick V. Bradley. He was reelected to the two succeeding Congresses and served from August 26, 1947, until his resignation November 4, 1952. He was elected to the United States Senate in 1952 to fill the vacancy caused by the death of Arthur H. Vandenberg and served from November 5, 1952, to January 3, 1953. He was also elected in 1952 for the term commencing January 3, 1953. He defeated Blair Moody in both elections. He served until January 3, 1959, having been defeated for reelection to a second term in 1958 by Philip Hart. He engaged as an industrial consultant and international securities executive. He was a member of the American Battle Monuments Commission and resided in Queenstown, Maryland, until his death at Walter Reed Army Hospital, Washington, D.C.. He is interred in Section 30 of Arlington National Cemetery, Ft. Myer, Virginia.