Blue, the oldest of six children, was born and raised in Mansfield, Louisiana. His father worked as a laborer in an iron foundry. In high school he pitched for the baseball team and also was the quarterback for the football team. In his senior year of high school, he threw for 3,400 yards and completed 35 touchdown passes while rushing for 1,600 yards in football. Also in his senior year, Blue threw a no-hitter. In seven innings pitched one game, Blue had 21 strikeouts. He received several offers to play college football, but after his father died suddenly Blue signed a contract with the Oakland A's.
After Blue's breakthrough season in 1971, he and Athletics owner Charlie Finley clashed over his salary. Blue held out, missing much of the year, and ended up with a 6–10 record. He didn't make the Athletics' post-season starting rotation, instead pitching mainly in relief. Against the Cincinnati Reds in the 1972 World Series he made four appearances, including a save in Game 1, a blown save in Game 4, and a loss in a spot-starting role in Game 6.
Blue returned to form to win 20 games in 1973, 17 games in 1974, and 22 games in 1975, as an integral member of the Oakland Athletics' five straight American League Western Division pennants from 1971 to 1975, and three consecutive World Championships in 1972, 1973, and 1974. Perhaps his finest postseason performances were four innings of shutout relief work against the Detroit Tigers to save Game 5 of the 1972 American League Championship Series and a complete-game 1-0 shutout against the Orioles in Game 3 of the 1974 ALCS.
In 1976, baseball commissioner Bowie Kuhn vetoed an attempt by Oakland A's owner Charlie Finley to sell Blue to the New York Yankees, and in 1977, Kuhn cancelled a proposed trade of Blue to the Cincinnati Reds. In both instances, Kuhn said the trades would be bad for baseball because they would benefit already powerful teams without making them give up any significant talent in return. At the end of the 1976 season, nearly the entire A's roster of star players from Oakland's championship teams left with baseball's new free agency, or were traded off by Finley, leaving Blue, who was still under contract with Oakland, to mentor a new team of primarily rookies and other young players. In 1978, Blue was traded to the San Francisco Giants.
Blue battled drug addiction, "fat lines of cocaine", over the course of his career. After the 1983 season, he and former teammates Willie Wilson, Jerry Martin and Willie Aikens pleaded guilty to attempting to purchase cocaine. In 1985, he testified in the Pittsburgh drug trials. His troubles with substance abuse seem to haunt this former great pitcher, as he faced multiple DUI charges in 2005.
Blue remains active, working for numerous charitable causes including Safeway All Stars Challenge Sports, automobile donations, celebrity golf tournaments, and charities for the children.