A lifelong resident of Charleston, Jefferds was a graduate of Charleston High School and later earned his degree from Massachusetts Institute of Technology. Jefferds was employed with Bethelehem Steel in the Loop Program prior to serving in the U.S. Army. While in the military, he served in World War II and earned the rank of Lt. Colonel.
Upon his return home from the war, he worked alongside his father at the Kanawha Drug Company. In 1947, he embarked on a partnership with Julius T. Moore Sr. and founded Jefferds and Moore, which became Jefferds Corporation. He served as its president until 1991 and as chairman until his death.
Jefferds is survived by his son Joseph C. Jefferds III, daughters Marion Jefferds Sinclair and Oliva Polk Jefferds, all of Charleston, three grandchildren and two great-grandchildren. He is also survived by his two sisters Caroline Jefferds Dixon and Agnes Jefferd Sonntag.