Joe Purcell was born in Warren, Arkansas. He graduated from Little Rock Junior College. He served in the United States Army during World War II.
He graduated from the University of Arkansas law school in 1952 and practiced law in Benton, Arkansas.
From 1955-1959 he served as a city attorney in Benton. He served as a municipal judge from 1959 until 1966 when he was elected Attorney General of Arkansas where he served from 1967 to 1971. He was defeated in the Democratic primary for Governor in 1970.
Purcell served as Lieutenant Governor of Arkansas from 1975 until 1981.
He became Governor of Arkansas for six days filling the unexpired term of then Senator-elect David Pryor.
Purcell resides in Benton, Arkansas.