Woodruff attended Wheeler High School in Wheeler, Mississippi and was drafted by the Texas Rangers in the fifth round of the 2011 MLB draft out of high school. He did not sign with the Rangers and attended Mississippi State University to play college baseball. In 2014, his junior season, he went 1-3 with a 6.75 ERA in 37 innings. In 2012, he played collegiate summer baseball with the Harwich Mariners of the Cape Cod Baseball League. After his junior year he was drafted by the Milwaukee Brewers in the 11th round of the 2014 MLB Draft. Woodruff made his professional debut that year with the Helena Brewers and spent the whole season there, going 1–2 with a 3.28 ERA in 14 games. He pitched 2015 with the Brevard County Manatees, compiling a 4–7 record and 3.45 ERA in 21 games, and started 2016 there. In May, he was promoted to the Biloxi Shuckers. In July, his brother died following an ATV accident. In his first start since his brother's death, Woodruff threw six shutout innings allowing one hit with nine strikeouts as well as hitting a home run. Woodruff ended 2016 with a combined 14-9 record and 2.68 ERA in 28 starts between both teams. Woodruff started the 2017 season playing with the Colorado Springs Sky Sox. The Brewers promoted Woodruff to the major leagues on June 13. However, he injured himself warming up, and was placed on the disabled list. The Brewers recalled Woodruff to make his debut on August 4. He was optioned back to Colorado Springs on August 20 and recalled once again on September 1. In eight starts for Milwaukee he was 2–3 with a 4.81 ERA, and in 16 starts for Colorado Springs he pitched to a 6-5 record and 4.30 ERA. MLB.com ranked Woodruff as Milwaukee's third best prospect going into the 2018 season. He began 2018 with Milwaukee, but was optioned to Colorado Springs in early April. He opened Game 1 of the NLDS against the Colorado Rockies, pitching three scoreless innings in the Brewers' eventual 3–2 win. In Game 1 of the 2018 National League Championship Series against the Los Angeles Dodgers, Woodruff hit a home run off of Clayton Kershaw. He became the 22nd pitcher and the 3rd relief pitcher in postseason history to accomplish the feat. Woodruff also became the only pitcher in baseball postseason history to hit a home run lefty on lefty.
