Taylor was born in Tipton County, Tennessee, located north of Memphis, to Bassil Gray Taylor, who earned the family livelihood as a farmer and carpenter, and the former Lennie Fee Shinault. He was educated in public schools and attended Memphis State University, then Memphis State College, from 1937 to 1939. He taught in a one-room school in Tennessee from 1939 until 1941.

With the attack on Pearl Harbor, Hawaii, Taylor joined the United States Air Force (then the Army Air Force). He flew seventy missions as bombardier-navigator with the Twelfth Bomb Group in the China-Burma theater. He attained the rank of first lieutenant and was awarded the Distinguished Flying Cross, the Air Medal, and three battle stars.

On his discharge from the armed forces in 1945, Taylor married the former Helen Friday (born 1923), of North, South Carolina, a small town near Orangeburg. She was the daughter of the attorney Edward Brodie Friday and the former Ora Barksdale Coleman. The couple had three children, Joe G. Taylor, Jr. (born 1952), Harriet Eva Taylor (born 1955), and Edward Coleman Taylor (born 1959).

After the war, Taylor obtained his bachelor of arts and Master of Arts degrees from Memphis State in 1947 and 1948, respectively. He threafter obtained the Ph.D. degree in history from Louisiana State University in Baton Rouge in 1951. He taught at Nicholls State University in Thibodaux (the Junior College) from 1950 to 1953, prior to a four-year commitment as the historian at the Air Force Research Studies Institute at Maxwell Air Force Base near Montgomery, Alabama.

Taylor returned to teaching at Southeastern Louisiana University (then College) in Hammond for the 1957–1958 term. Then he returned to Nicholls State from 1958—1963, when he became professor at McNeese, a position that he held until his death twenty-four years later.

At McNeese, Taylor chaired the history department from 1968 to 1983. He was then the dean of the College of Liberal Arts from 1983 until his death.

Taylor produced five monographs and four essays on Air Force history. Otherwise, he concentrated on Louisiana and the South. His works included Negro Slavery in Louisiana (1963) and Louisiana Reconstructed, 1863–1877 (1974), which won the L. Kemper Williams Prize and the Louisiana Literary Award. A later work was his social history on southern hospitality entitled Eating, Drinking, and Visiting in the South (1982). Taylor was one of three coauthors of Louisiana: The Pelican State, a middle school textbook which traces the development of the state from earliest times to the 1980s.

Taylor also authored book reviews in twenty historical journals and thirty reviews in Louisiana History alone. One of Taylor's acclaimed reviews was "The Many Interests of T. Harry Williams" in the March 1984 edition of Reviews in American History. Williams was the preeminent historian at LSU prior to his death in 1979.

Taylor was the president of the Louisiana Historical Association in 1967. He received the McNeese "Distinguished Teaching Award" in 1979. He received the "Award of Merit" from the American Association for State and Local History in 1984. He was a member of the executive council of the Southern Historical Association for the last two years of his life. He was named Louisiana "Humanist of the Year" in 1986. His associations included Phi Kappa Phi, Phi Alpha Theta, the American Historical Association, the Organization of American Historians, the Louisiana Historical Association. He was an elder in the Presbyterian Church.

Taylor died in Lake Charles. He is interred in Robinson Cemetery near the Gainsville Community in Tipton County. Taylor's papers are in McNeese's Lether Edward Frazar Library.