The New York Yankees selected Reeves in the tenth round, with the 303rd overall selection, of the 2015 MLB draft.[2] He made his professional debut in 2015 with the Staten Island Yankees where he pitched to a 1–1 record and 3.08 ERA in 13 games, and began the 2016 season with the Charleston RiverDogs.[5][6] He received promotions to the Tampa Yankees[7] and the Trenton Thunder during the season.[8] In 32 total games between the three teams, he posted a 6–2 record with a 2.22 ERA and a 0.91 WHIP. In 2017, he played for both Tampa and Trenton, posting a combined 1.96 ERA with 51 strikeouts in 46 innings pitched between both teams.[9]
Reeves split the 2018 season between the Triple-A Scranton/Wilkes-Barre RailRiders and Double-A Trenton, pitching to a cumulative 2-2 record and 2.88 ERA with 72 strikeouts in 56.1 innings of work. The following year, Reeves split time between Double-A Trenton and High-A Tampa, posting a stellar 7-2 record and 1.87 ERA with 83 strikeouts in 67.1 innings pitched. Reeves did not play a minor league game in 2020 due to the cancellation of the minor league season because of the COVID-19 pandemic.[10]
On January 6, 2021, Reeves was traded to the San Diego Padres in exchange for Greg Allen.[11] Reeves made 40 appearances split between the Triple-A El Paso Chihuahuas and the Double-A San Antonio Missions, recording a 3-0 record and 5.65 ERA with 75 strikeouts in 51.0 innings pitched.
On May 3, 2022, Reeves signed with the Chicago Dogs of the American Association of Professional Baseball.[12] Reeves pitched in 22 games for the Dogs, logging a 1-1 record and 3.42 ERA with 35 strikeouts in 26.1 innings pitched, and was named an All-Star for the team.[13]
In 2023, Reeves appeared in 2 games for Chicago, surrendering 5 runs (3 earned) on 3 hits and 3 walks with 3 strikeouts in 2.0 innings pitched. He was released by the Dogs on May 18, 2023.[14]
On May 19, 2023, Reeves signed with the Kane County Cougars of the American Association of Professional Baseball.[14] In 10 games for the Cougars, he logged a 5.63 ERA with 9 strikeouts in 8.0 innings pitched. On July 15, Reeves was released by the Cougars.[15]