Radcliffe was raised in Mobile, Ala., and he and his brother Alec, also later a Negro league player, relocated to Chicago after World War I. Radcliffe began his career in the Negro leagues with the Detroit Stars in 1928; he batted .316 in his 1929 season with them. He joined the St. Louis Stars in 1930, batting .283 and pitching 10 wins and 2 losses, and in 1931 he batted .298 and pitched 9–5 for the Homestead Grays. In 1932, playing for the Pittsburgh Crawfords, Radcliffe batted .325 and went 19–8 in pitching. That same year, writer Damon Runyon (Runyon, Damon) dubbed him “Double Duty” after witnessing him play one game as a catcher and the next as a pitcher against the New York Black Yankees. Radcliffe played in the leagues' East-West All-Star Game six times, three as a pitcher and three as a catcher. Over his entire career he played for 13 Negro league teams in addition to spending time on numerous semiprofessional teams, some of them integrated.

Radcliffe managed the Memphis Red Sox from 1937 to 1938 and the Chicago American Giants in 1943 and 1950 while simultaneously playing for those teams. He also staged frequent exhibition games against teams in the white leagues. Radcliffe retired in 1954, but in the 1960s he returned to serve as a scout for the Cleveland Indians.

As well as demonstrating versatility on the field, Radcliffe was known for his humour; the chest protector that he wore while functioning as a catcher was emblazoned with the phrase “Thou Shalt Not Steal” (one of the Ten Commandments), referring to his intention of preventing the other team from stealing bases. When interviewed by sports journalists later in life, he often related hyberbolic tales of the extraordinary athletic feats that he and other Negro league players had accomplished in addition to more sober stories of the racism that they had encountered. From age 99 until his death, Radcliffe each year threw the ceremonial starting pitch at a Chicago White Sox game to celebrate his birthday.