Amateur career Puckett attended
De La Salle High School in
Concord, California. He played
baseball and
American football for De La Salle,
pitching for the baseball team and playing
quarterback and
safety in football. The
Oakland Athletics selected Puckett in the 35th round of the
2013 MLB draft, but he did not sign with Oakland. Puckett then enrolled at
Pepperdine University and played
college baseball for the
Pepperdine Waves. In 2015, he played
collegiate summer baseball with the
Chatham Anglers of the
Cape Cod Baseball League. In 2016, his junior year, Puckett pitched innings without allowing a run, the third-longest scoreless streak in
NCAA Division I history. He finished his junior year with a 9–3 win–loss record, a 1.27 ERA, and 95 strikeouts to 26 walks in innings. Puckett was named a First Team
All-American by the
American Baseball Coaches Association,
Baseball America, and
Collegiate Baseball Newspaper. He was named a Second Team All-American by the
National Collegiate Baseball Writers Association.
Kansas City Royals The
Kansas City Royals selected Puckett in the second round, with the 67th overall selection, of the
2016 MLB draft. He signed with the Royals, receiving a $1.2
signing bonus. After signing, he was assigned to the
AZL Royals, and after pitching to a 3.86 ERA in two games, he was promoted to the
Lexington Legends where he posted a 2–3 record and 3.66 ERA in 11 games. He began the 2017 season with the
Wilmington Blue Rocks.
Chicago White Sox The Royals traded Puckett and Andre Davis to the
Chicago White Sox for
Melky Cabrera on July 30, 2017. The White Sox assigned him to the
Winston-Salem Dash. In 25 total games started between Wilmington and Winston-Salem, Puckett posted a 10–7 record with a 3.98 ERA. He missed the entire 2018 season with elbow pain, and elected to undergo
Tommy John surgery on March 13, 2019. Puckett did not play in a game in 2020 due to the cancellation of the minor league season because of the
COVID-19 pandemic.
Atlanta Braves On December 10, 2020, the
Atlanta Braves selected Puckett in the minor league phase of the
Rule 5 draft. Puckett split the 2021 season between the High-A
Rome Braves and the Double-A
Mississippi Braves, accumulating a 4–6 record and 2.90 ERA with 72 strikeouts in innings pitched across 20 games. In 2022, Puckett returned to Mississippi. In 33 games, he struggled to a 2–5 record and 7.36 ERA with 74 strikeouts in innings of work. Puckett elected free agency following the season on November 10, 2022.
Seattle Mariners On February 8, 2023, Puckett signed a minor league contract with the
Seattle Mariners organization. In 47 appearances split between the Double–A
Arkansas Travelers and Triple–A
Tacoma Rainiers, he accumulated a 6–4 record and 4.52 ERA with 54 strikeouts across innings pitched. Puckett elected free agency following the season on November 6.
Charros de Jalisco On April 23, 2024, Puckett signed with the
Charros de Jalisco of the
Mexican League. In 18 appearances for Jalisco, he compiled a 3–0 record and 1.02 ERA with 17 strikeouts and 3 saves across innings pitched.
Chicago Cubs On January 30, 2025, Puckett signed a minor league contract with the
Chicago Cubs. He made 46 appearances out of the bullpen for the Double-A
Knoxville Smokies, compiling a 3-6 record and 3.35 ERA with 46 strikeouts and 15
saves across 51 innings pitched. Puckett elected free agency following the season on November 6.
Charros de Jalisco (second stint) On February 24, 2026, Puckett signed with the
Charros de Jalisco of the
Mexican Leagus. ==Personal life==