Swarzak attended Nova High School in Davie, Florida. As a sophomore, Swarzak pitched to an 11–1 win–loss record with a 1.16 earned run average and 120 strikeouts and was named to the All-County team and second team All-State. In 2003, he finished 14–1 with 142 strikeouts. In his senior season, in which he went 14–2, with 147 strikeouts, Swarzak was named to the 2004 All-County and Class 5A All-State teams. He had committed to attend Louisiana State University to play college baseball for the LSU Tigers, but instead chose to sign with the Twins on June 22, 2004, for a $575,000 bonus.
The Minnesota Twins selected Swarzak in the second round, with the 61st overall selection, in the 2004 Major League Baseball draft. Swarzak was #15 on the Baseball America Top Gulf Coast League Prospects list in 2004. He was Midwest LeaguePitcher of the Week, the Twins' Pitcher of the Month, Midwest League All-Star, and #8 on the Baseball America Top Midwest League Prospects list in 2005. In 2006, he was Florida State League Pitcher of the Week and a FSL Post-Season All-Star. Swarzak was one of the top rated prospects in the Twins' farm system before a fifty-game suspension for violation of Minor League drug policy on April 20, 2007 sidetracked his career. He tested positive for marijuana. After having started the season with the Double A New Britain Rock Cats, upon his reinstatement from the restricted list on June 11, he was reassigned to the Class A AdvancedFort Myers Miracle. After three games with Fort Myers, he returned to New Britain. He began the 2008 season with the Rock Cats, and went 3–8 with a 5.67 earned run average. After a promotion to Triple-A, his record actually improved to 5–0 with a 1.80 ERA in seven starts. He was added to the Twins' 40 man roster, and spent his first spring with the Twins in 2009. Following Spring training, he was reassigned to Rochester. Swarzak suffered from a lack of run support in Rochester to start the season. Despite an ERA of 1.59 in his first three starts, his record stood at 0–3. His record improved to 3–4 with a 2.25 ERA when he got the call to the majors on May 20. He filled in the starting rotation for the injured left-handed starter Glen Perkins. Swarzak made his major league debut for the Twins on May 23, 2009 in a home game against the Milwaukee Brewers. He pitched seven shutout innings, giving up five hits and two walks while striking out three. The Twins won the game 6–2, earning Swarzak his first major league win. After a line drive broke his foot, Swarzak's 2010 season was statistically awful as he spent the whole year in the minors. His ERA finished at 6.21 in AAA Rochester. Swarzak rebounded in 2011, contributing both in long relief and in spot starts for the Twins. He pitched a total of 102 innings, going 4–7 in 27 games. In 2012, Swarzak started five games for the Twins while making 39 appearances out of the bullpen, pitching to a collective 96 innings of work. Swarzak began 2013 on the disabled list with fractured left ribs he suffered while "wrestling around a little bit." He was activated on April 7 and used primarily as a long reliever for the rest of the season. In 48 games, he went 3–2 with a 2.91 ERA, striking out 69 in 96 innings. On November 25, 2014 the Twins announced that Swarzak had been outrighted off the 40-man roster and elected free agency.
Cleveland Indians
He joined the Cleveland Indians on a minor league contract for the 2015 season,
Doosan Bears
He was released in May and signed with the Doosan Bears of the Korea Baseball Organization. Swarzak filled the foreign player roster spot formerly held by Yunesky Maya. He worked mainly as a starting pitcher in Korea and added a slider to his arsenal of pitches.
Swarzak signed a minor league contract with the New York Yankees on February 5, 2016. He began the 2016 season with the Triple-A Scranton/Wilkes-Barre RailRiders, and was promoted to the major leagues on June 7. At the end of the season, Swarzak elected free agency over an assignment to Scranton/Wilkes-Barre.
Swarzak signed a two-year contract with the New York Mets on December 15, 2017 worth over $14 million. On April 3, the Mets placed Swarzak on the disabled list with an oblique strain and recalled Hansel Robles. Swarzak was activated from the disabled list on June 5 after appearing in three rehab games with the Triple-A Las Vegas 51s.
On May 20, 2019, Swarzak was traded to the Atlanta Braves in exchange for Arodys Vizcaíno and Jesse Biddle. He became a free agent following the 2019 season.
