[4] After his junior year, the San Francisco Giants selected Woods in the eighth round of the 2016 MLB draft.
[2][5] He spent his first professional season with both the AZL Giants and the Low-A Salem-Keizer Volcanoes, posting a combined 1–2 record and 3.34 ERA in 35 total innings.
[6] On December 20, 2017, the Giants traded Woods, Denard Span, Christian Arroyo, and Matt Krook to the Tampa Bay Rays in exchange for Evan Longoria and cash considerations.
Woods returned to pitch in 2019, spending the year with the High-A Charlotte Stone Crabs and compiling a 9–3 record with a 1.88 ERA over 18 games (12 starts), striking out 79 over 86+1⁄3 innings.
[8] On July 21, 2020, Woods was returned to the Rays organization, but was traded back to the Royals the same day in exchange for a player to be named later.
Woods split the 2022 campaign between Northwest Arkansas and the Triple-A Omaha Storm Chasers, accumulating a 4.28 ERA with 75 strikeouts across 41 relief appearances.