Undrafted in the 2017 Major League Baseball draft, Beeter enrolled at Texas Tech University to play college baseball for the Texas Tech Red Raiders. He suffered an arm injury in the fall of freshman year at Texas Tech, and underwent Tommy John surgery, thus forcing him to miss the 2018 season.[3] He returned healthy as a redshirt freshman in 2019, going 0–3 with a 3.48 ERA over 20+2⁄3 relief innings, striking out forty.[4] In 2020, his redshirt sophomore season, Beeter moved into the starting rotation, and was named the starting pitcher for Texas Tech's season opener.[5] Beeter went 2–1 with a 2.14 ERA over four starts before the college baseball season was cut short due to the COVID-19 pandemic.[6]
To begin the 2021 season, he was assigned to the Great Lakes Loons of the High-A Central.[9] On July 24, Beeter pitched two innings of a combined no-hitter against the Lake County Captains alongside Bobby Miller, Jake Cantleberry, and Cameron Gibbens.[10] After making 22 starts and pitching to a 0–4 record, a 3.13 ERA, and 55 strikeouts over 37+1⁄3 innings, he was promoted to the Tulsa Drillers of the Double-A Central in mid-August.[11] Making five starts with Tulsa, Beeter went 0–2 with a 4.80 ERA over 15 innings.[12] He returned to Tulsa to begin the 2022 season.[13]
On November 14, 2023, the Yankees added Beeter to their 40-man roster to protect him from the Rule 5 draft.[21] On March 25, 2024, the Yankees announced that Beeter had earned one of the team's final Opening Day bullpen roles alongside Nick Burdi.[22] He made his MLB debut on March 29, pitching one inning of relief without allowing a run, and was optioned to Triple-A Scranton/Wilkes-Barre the next day.[23]
