Criswell was assigned to the Double-ARocket City Trash Pandas at the beginning of the 2021 minor league season.[7] Criswell made 12 starts for Double-A Rocket City, going 6–4 with a 3.71 ERA and 85 strikeouts. On July 31, Criswell was promoted to the Triple-A Salt Lake Bees. After going 2–1 with a 3.98 ERA and 27 strikeouts through four starts, on August 27, the Angels selected Criswell's contract.[8] He made his debut the same night, giving up three runs in 1.1 innings pitched.[9] He was optioned back to Salt Lake the next day.[10]
On April 7, 2022, Criswell was placed on the 10-day injured list with a right shoulder strain[11] and was moved to the 60-day injured list the next day to make room on the 40-man roster for Kyle Tyler.[12]
Tampa Bay Rays
On July 16, 2022, Criswell was claimed off waivers by the Tampa Bay Rays.[13] He was designated for assignment on July 19. He cleared waivers and was sent outright to the Triple-A Durham Bulls on July 21.[14] He made 3 starts for Durham on the year, posting a 3.09 ERA with 10 strikeouts in 11.2 innings pitched.
Criswell was selected back to the active roster as a COVID-19 replacement player on September 12, 2022. He tossed 3.1 innings against the Toronto Blue Jays, striking out 4 and walking one while allowing one earned run on two hits. He was removed from the 40-man roster and returned to Triple-A the next day.
Criswell was assigned to Durham to begin the 2023 season, and made 3 starts before he had his contract selected to the active roster on April 17, 2023.[15] In 10 games for the Rays, he posted a 5.73 ERA with 27 strikeouts across 33.0 innings of work. On November 14, Criswell was designated for assignment after multiple prospects were added to the roster.[16]
Boston Red Sox
On December 13, 2023, the Boston Red Sox signed Criswell to a one year, $1 million contract.[17] Criswell was optioned to the Triple–A Worcester Red Sox to begin the 2024 season.[18] He was recalled to Boston on April 13 to make a start against the Los Angeles Angels.[19] In his Red Sox debut, Criswell pitched four innings; allowing five hits, two earned runs, a walk and four strikeouts as the Red Sox went on the defeat the Angels 7–2.[20]
With injuries to Red Sox starting pitchers Brayan Bello, Nick Pivetta and Garrett Whitlock, Criswell remained in the Red Sox starting rotation.[21][22] On April 24, Criswell earned his first win with the Red Sox after pitching five scoreless innings in the 8–0 victory over the Cleveland Guardians.[21] On June 1, Criswell pitched five-plus innings in the Red Sox 6–3 win over the Detroit Tigers.[23] On June 18, Criswell was optioned to Triple-A Worcester to make room for pitcher Chris Martin who was activated from the injured list.[24][25] He was recalled to Boston on July 12.[26] After rejoining the team, Criswell showcased his versatility as both a spot-starter and high-leverage relief pitcher.[27]
On December 10, 2022, Criswell married his girlfriend Alex.[29] In May 2023, the couple announced that they were expecting a child.[30] On November 9, 2023, the couple welcomed a son named Cash Alexander Criswell.[31]
