Boyd had one of the more colorful personalities of his generation and a quotable outlook that made him memorable long after his career ended. He attended Jackson State University. Being selected by the Boston Red Sox in the 16th round of the 1980 amateur draft, Boyd made his debut in the 1982 season. He pitched 10 years in the majors before blood clots in his right arm ended his career.

In a 10-season career, Boyd collected a 78-77 record with 799 strikeouts and a 4.04 ERA in 1389.2 innings.

From 1983-85 Boyd won 31 games for the Sox, with a high 15 victories in 1985. In the same season, he posted career-highs in games started (35), complete games (13), strikeouts (117) and innings pitched (272.1). In 1986 he won 16 games (a career-high), but after three disappointing years with Boston, he signed with the Expos as a free agent after the 1989 season.

In 1990 Boyd won 10 games with a career-best 2.93 ERA. When the Rangers acquired him from Montreal in the 1991 midseason, it looked like a deal which might lead to a division title, and though Boyd's work with the Expos before coming to Texas wasn't as good (6-8, 3.52), it was plenty good enough for the pitching-poor Rangers. That was the plan, but Boyd turned out to be a disaster. In 12 starts he posted a 2-7 record with a 6.68 ERA (the highest of his career) and allowed 81 hits in only 62 innings. Boyd was a free agent when the season ended, and after turning down some offers for relief duties, he retired for good. Between the 1990s and 2000s, Boyd has pitched in the minors, Puerto Rico and Mexico.

Boyd's nickname comes from his beer-drinking days in his hometown of Meridian, Mississippi, where beer is referred to as "oil."

In November 2005, Boyd was indicted by a federal grand jury in Mississippi for threatening a former girlfriend (who was also a business associate) as well as her son. On November 14, 2005, Boyd surrendered to F.B.I. agents in Tupelo, Mississippi.