He has previously played in Major League Baseball (MLB) for the Boston Red Sox, Tampa Bay Rays, Colorado Rockies, and Pittsburgh Pirates.

[2] A reliable reliever during the 2013 season, Beeks allowed the game-tying and go-ahead runs on consecutive wild pitches during an intentional walk in the 7th inning against the Kansas State Wildcats in the Manhattan Regional.

[4] Beeks returned to Arkansas for the 2014 season as the opening day starter, starting 13 games with a 6–4 record and 1.98 earned run average (ERA).

[7] The Red Sox named him their Minor League Pitcher of the Year[8] after he posted a combined 11–8 record, 3.29 ERA, and 1.21 WHIP in 26 games started between the two teams.

[11] Beeks was promoted to Boston's active roster on June 7, 2018,[12] in order to make his MLB debut in a start against the Detroit Tigers.

[15] On July 25, 2018, the Red Sox traded Beeks to the Tampa Bay Rays in exchange for right-handed pitcher Nathan Eovaldi.

[20] On August 25, 2020, Beeks tore his ulnar collateral ligament while pitching against the Baltimore Orioles, ending his season and requiring Tommy John surgery.