Cleveland selected him in the first round of the 1986 draft. The highly touted player was brought up almost immediately in 1986 and had moderate success, going 5–2 in his rookie year that saw him pitch nine games with one being a complete game while having a 4.23 ERA. In 1987, he started the season 3-8 and then injured his elbow. ending his season after 16 appearances (15 starts) with a 5.10 ERA. He returned in 1988 and over the next four years displayed good form on a poor-performing Indians ballclub. His record from 1988 to 1991 was 52–43, posting an
earned run average below 4.00 in three of the four seasons. His best season was 1988 when he went 18–14 with a 3.20 ERA. He
struck out 180 and
walked only 45. The next year, he was named to the American League
All-Star team. Swindell was traded to Cincinnati after the 1991 season and spent one year with the Reds. He returned to his native Texas as a free agent in 1992 with the Astros. At that point, his effectiveness began to wane. In three and a half years, he was 30–35 with an ERA over 4.00. After another stint with Cleveland in 1996, he signed with Minnesota where he reinvented himself as a
reliever. As a relief pitcher, Swindell pitched well for the Twins and Red Sox before he signed with Arizona. He was effective for the Diamondbacks and was a part of the
2001 championship squad. He faced eighteen total batters and allowed one run total through the whole postseason. In 2002, he retired from baseball after 17 seasons, finishing his career by getting only one out in four batters faced in two games of the 2002 NLDS, allowing four runs (one earned). ==Post-playing career==