Graveman was selected in the 8th round, 235th overall, by the Blue Jays in the 2013 MLB draft. He received a signing bonus of $5,000, and was assigned to the Class-A Lansing Lugnuts. Graveman would pitch to a 1–3 record and a 4.31 earned run average over 39 innings in 2013. He began the 2014 season with Lansing, but was promoted to the High-A Dunedin Blue Jays after making 4 starts for the Lugnuts and posting a 2–0 record with a 0.34 ERA, including a near no-hitter over the Beloit Snappers. In Dunedin, he compiled an 8–4 record in 16 starts, with a 2.23 ERA and 64 strikeouts. Graveman was promoted to the Double-A New Hampshire Fisher Cats and made just 1 start, a 6-inning win over the Binghamton Mets, before being promoted to the Triple-A Buffalo Bisons. In his Triple-A debut, he took the loss, pitching 6 innings in a 2–1 loss to the Norfolk Tides. Graveman would allow only 1 earned run in his following 3 starts, bringing his ERA to 1.04 through 26 innings with Buffalo. He finished the 2014 minor league season with a 14–6 record over 167 innings, with an ERA of 1.83, 115 strikeouts, and a WHIP of 1.03. He also gave up only 2 home runs and issued 31 walks, for a BB/9 of 1.7. On September 3, Graveman was named to Baseball America's First Team All-Stars for 2014.
On September 1, 2014, Graveman was called up to the Blue Jays as a part of the September roster expansion. He made his MLB debut on September 5, against the Boston Red Sox. 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 4 innings pitched.
Oakland Athletics
On November 28, 2014, Graveman was traded to the Oakland Athletics, along with Brett Lawrie, Sean Nolin, and Franklin Barreto, for Josh Donaldson. 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. Graveman was called back up to the A's on May 23. He finished his rookie season with a 6–9 record and 4.05 ERA in 21 starts. On April 20, 2016, Graveman became the first pitcher to bat at the new Yankee Stadium and struck out after 3 pitches. Graveman batted in the clean-up spot, and became the first pitcher to bat clean-up since Babe Ruth in. Graveman became the A's only consistent starter for the 2016 season, notching 10 wins in 31 starts. With Sonny Gray starting the 2017 season on the DL with a lat strain, Graveman was chosen to start on opening day, the first opening day start of his career. He pitched six innings, struck out seven and took the win over the Los Angeles Angels. On April 17, 2017, Graveman was placed on the 10-day disabled list due to a right shoulder strain. His first game back with the A's, April 27, Graveman executed an unassisted double play. The previous such play made by an Oakland pitcher was on July 11, 1971, by Blue Moon Odom, who happened to be in attendance at Angel Stadium and witnessed Graveman make the play. After starting a couple of games after being activated, Graveman was placed again on the disabled list on May 29 due to shoulder soreness. On March 20, Graveman was announced as the 2018 opening day starter for the second consecutive year. After starting the season 0–5 with an 8.89 ERA, Graveman was demoted to Triple-A on April 26. Graveman underwent Tommy John surgery on July 24, 2018. He was non-tendered by the Athletics on November 30, 2018, and became a free agent.
Graveman signed a one-year contract with an option for the 2020 season with the Chicago Cubs on December 23, 2018. He became a free agent after the season.
Seattle Mariners
On November 26, 2019, Graveman signed a one-year contract with the Seattle Mariners. Graveman made the Mariners Opening Day roster in 2020. On July 27, 2020, he made his Mariners debut.
Scouting report
Graveman is a sinkerballer, throwing his sinker between 91 and 96 MPH. He also throws a cutter, a slider, and a change-up.
