Young was born in Pasadena, California in 1958. He attended the University of California Los Angeles. While at UCLA, he was drafted by the Seattle Mariners, in the second round of the 1980 amateur draft. He made his major league debut three years later with the Mariners, eventually winning 11 games over 2031/3 innings, with a 3.27 earned run average, good enough to rank in the top ten for ERA that season. He represented the Mariners in the 1983 Major League Baseball All-Star Game, where he pitched a scoreless 8th inning facing Johnny Bench, Darrell Evans and Pedro Guerrero.
Young, however, struggled to replicate that success, underwent "Tommy John surgery" and was traded twice, from the Mariners to the Los Angeles Dodgers, then to the Oakland Athletics in a three-team trade with the New York Mets, appearing in a game in relief during the 1989 American League Championship Series. Eventually, Young hit free agency and signed with the Boston Red Sox.
Young pitched for the Red Sox for two seasons before being released days before the start of the 1993 season. He became part of baseball history during his tenure with the Red Sox. On April 12, 1992, Young faced the Cleveland Indians in the first game of a doubleheader, allowed two runs on seven walks and an error by shortstop Luis Rivera en route to the fourth no-hitter by a losing pitcher (see No-hitter#No-hitters in a losing cause). On that day Roger Clemens pitched a two-hit shutout in the second game of the double header, giving Young and Clemens the Major League Baseball record for the least number of hits (2) allowed in a doubleheader. While Young sent the ball to the Baseball Hall of Fame in Cooperstown, New York, Major League Baseball, in a rule created prior to the season, did not recognize the performance as a true no-hitter, as Young, playing for the losing team on the road, only pitched eight innings in his complete game loss. According to Seymour Siwoff, who was on Baseball's Committee for Statistical Accuracy, the feat could not be listed with the "pure" no-hitters because "Young didn't get the chance to go out and pitch the ninth...who knows what would have happened if he did." Had the no-hitter been officially recognized, it would have been the first no-hitter by a Boston pitcher since Dave Morehead did so in 1965, also against the Indians, and was the fifteenth time, at that point, that a Red Sox pitcher had completed a game without allowing a hit.
Young was released by the Red Sox in 1993, appeared in 22 games for the Indians in 1993, and finally spent a month with the Syracuse Chiefs, a minor league team in the Toronto Blue Jays organization, before being released a final time in September 1993.