 Paxton was originally drafted out of Oakhaven High School in Memphis by the New York Yankees in the 1971 Major League Baseball draft, but did not sign, choosing instead to attend Memphis State.After four seasons with the Memphis Tigers, in which he was a four-year letter winner under head coach Bobby Kilpatrick, Paxton was drafted by the Boston Red Sox in the 1975 Major League Baseball draft.He debuted with the Red Sox on May 25, , starting the second game of a doubleheader with the Minnesota Twins, as he pitched 2.1 innings to take the loss.