Abbott signed with the Cubs and made his professional season with the Eugene Emeralds, compiling a 3.86 ERA over 14 innings. He pitched 2018 with the South Bend Cubs and Myrtle Beach Pelicans, going 8–6 with a 2.50 ERA in 22 starts, and 131 strikeouts in 115 innings, between the two clubs.[7]
He spent 2019 with the Tennessee Smokies,[8] pitching to an 8–8 record with a 3.01 ERA over 26 starts, striking out 166 (leading the league) over 146+2⁄3 innings.
Abbott did not play a minor league game in 2020 due to the cancellation of the minor league season caused by the COVID-19 pandemic. The Cubs added Abbott to their 40-man roster after the 2020 season.[9]
On June 5, 2021, Abbott was promoted to the major leagues for the first time.[10] He made his MLB debut that day, pitching two scoreless innings of relief against the San Francisco Giants. In the game, he also notched his first major league strikeout, punching out Giants pitcher Kevin Gausman. On June 20, 2021, the Cubs optioned Abbott to AAA Iowa.[11] On October 1, Abbott collected his first career hit, a single off of St. Louis Cardinals starter Dakota Hudson.[12]
On April 21, 2022, Abbott was traded to the San Francisco Giants for cash considerations. Abbott was claimed off waivers by the Washington Nationals on May 4.[14] He made 16 appearances (9 starts) for Washington down the stretch, posting an 0–5 record and 5.25 ERA with 45 strikeouts in 48 innings pitched.
Abbott was optioned to the Triple-A Rochester Red Wings to begin the 2023 season.[15] In 22 games for the Nationals, he struggled to a 6.64 ERA with 40 strikeouts across 39+1⁄3 innings of work. On November 14, 2023, Abbott was designated for assignment by Washington after multiple prospects were added to the 40–man roster.[16] He was non-tendered and became a free agent on November 17.
Seattle Mariners
On January 9, 2024, Abbott signed a minor league contract with the Seattle Mariners.[17] He made one start for the Triple–A Tacoma Rainiers before being released by the Mariners organization on April 3.[18]
Chicago White Sox
On April 12, 2024, Abbott signed a minor league contract with the Chicago White Sox.[19] He became a free agent after the 2024 season.[20] On July 1, 2024, Abbott was named the International League Pitcher of the Week.[21]