Stashak played for the rookie–level Elizabethton Twins, posting a 5-2 record with a 3.43 ERA in 44+2⁄3 innings.[6] His 2016 season was split between the Single–A Cedar Rapids Kernels and the High–A Fort Myers Miracle, posting a 10-5 record with a 2.80 ERA over 121+1⁄3 innings.[6] He split the 2017 season between the rookie–level Gulf Coast Twins, Fort Myers, and the Double–A Chattanooga Lookouts, combining to go 4-4 with a 3.60 ERA in 94+1⁄3 innings.[6] His 2018 season was split between Fort Myers and Chattanooga, going a combined 2-1 with a 2.87 ERA in 59+2⁄3 innings.[6] He split the 2019 minor league season between the Double–A Pensacola Blue Wahoos and the Triple–A Rochester Red Wings, going a combined 7–3 with a 3.21 ERA over 53 innings.[6]
On July 22, 2019, the Twins selected Stashak to the 40-man roster and promoted him to the major leagues for the first time.[7] He made his debut on July 23, pitching two scoreless innings of relief versus the New York Yankees.[8] In his rookie campaign, Stashak went 0–1 with a 3.24 ERA with 25 strikeouts over 24 innings of work.
In 2020 for the Twins, Stashak allowed three runs in seven innings for a 3.86 ERA before landing on the injured list.[9] In his first two seasons in the majors, Stashak struck out 42 batters while allowing only four walks.[10]
On June 25, 2021, Stashak was placed on the 60-day injured list with a left back disc injury.[11] He made 15 total appearances for Minnesota in 2021, struggling to a 6.89 ERA with 26 strikeouts in 15+2⁄3 innings pitched.
Stashak pitched in 11 games for Minnesota in 2022, working to a 3-0 record and 3.86 ERA with 15 strikeouts in 16+1⁄3 innings of work. On June 8, 2022, it was announced that Stashak would undergo season-ending surgery to repair a torn labrum in his right throwing shoulder.[12] On November 11, Stashak was removed from the 40-man roster and sent outright to the Triple–A St. Paul Saints; he elected free agency the same day.[13]
On August 10, 2023, Stashak's contract was purchased by the San Francisco Giants organization; he was subsequently assigned to the Triple–A Sacramento River Cats.[15] In five games for Sacramento, he struggled to a 12.60 ERA with four strikeouts in five innings of work. On November 16, Stashak was released by the Giants organization.[16]
On January 16, 2024, Stashak re-signed with the Giants on a minor league contract.[17] In 27 games for Triple–A Sacramento, he recorded a 5.45 ERA with 44 strikeouts and 2 saves across 36+1⁄3 innings pitched. Stashak was released by the Giants organization again on August 13.[18]
