He has previously played in MLB for the Toronto Blue Jays, Oakland Athletics, Seattle Mariners, Houston Astros, and Chicago White Sox.

[2] Graveman attended Benjamin Russell High School, where he posted a 6–3 win–loss record with a 1.19 earned run average (ERA) and 90 strikeouts over 63 innings pitched in his senior year.

[4][5] In his senior year at MSU, he made 16 starts, including 10 against Southeastern Conference teams, and posted a 4–4 record with a 2.81 ERA and 59 strikeouts.

[3] Graveman began the 2014 season with Lansing, but was promoted to the High-A Dunedin Blue Jays after making four starts for the Lugnuts and posting a 2–0 record with a 0.34 ERA, including a near no-hitter over the Beloit Snappers.

Graveman made 5 total appearances for the Blue Jays in 2014, and posted a 3.86 ERA, 4 strikeouts, no walks, and a 0.86 WHIP in 42⁄3 innings pitched.

[16] On November 28, 2014, Graveman was traded to the Oakland Athletics, along with Brett Lawrie, Sean Nolin, and Franklin Barreto, for Josh Donaldson.

[17] After opening the season as the fifth starter, Graveman was optioned to the Triple-A Nashville Sounds on April 26, 2015, after going 1–2 with an 8.27 ERA in 16.1 innings.

Following a nearly month-long stay on the injured list, he returned to the active roster as a relief pitcher,[2] citing less stress/pain on the tumor as the reason for his conversion.

On October 28, 2020, the Mariners declined their $3.5 million team option on his contract for the 2021 season, making him a free agent.

[35] On July 27, 2021, Graveman was traded along with Rafael Montero to the Astros in exchange for Abraham Toro and Joe Smith.

On the eighth pitch of the at bat, Toro hit a grand slam to right-center field which accounted for all of the runs scored in the game.

[39] In Game 5 of the 2021 World Series, Graveman became the final MLB pitcher to record an at-bat, due to the adoption of the designated hitter by the National League prior to the start of the 2022 season.

[41] On November 30, 2021, Graveman officially signed a three-year, $24 million contract with the Chicago White Sox.

On January 16, 2024, Graveman underwent right shoulder surgery, with reports stating that he would likely miss the entirety of the season.