Beachy attended Northwestern Senior High School in Kokomo, Indiana. He helped lead their baseball team to Indiana's 2004–2005 class AA state championship game. After the game, he was presented with the Indiana High School Athletic Association Mental Attitude Award. After high school, he attended Indiana Wesleyan University, where he played third base, first base, and pitched for the Indiana Wesleyan Wildcats.
Beachy was not selected in the 2008 Major League Baseball draft following his junior year of college, but signed with the Atlanta Braves as an undrafted free agent on July 22, 2008.
Beachy compiled a 4–3 record with one save and a 3.87 ERA in 76 2⁄3 innings of work spread over 35 appearances and three different teams in 2009. He struck out 64 batters and walked 19. Most of his time was spent with the Myrtle Beach Pelicans of the Class A advanced Carolina League.
In spring 2010, Beachy was one of six pitchers who took part in a spring mini-camp in which some of the Braves’ top minor leaguers took turns serving as backups for major league players in spring training games. He was the youngest minor leaguer in the mini-camp.
Beachy was moved into the starting rotation for the AA Mississippi Braves late June 2010. In his time as a AA player, he struck out 100 batters while allowing 53 hits and 22 walks in 27 games (73.2 innings) while maintaining a 1.47 ERA. He compiled a record of 3 wins and 1 loss. Opposing hitters hit .200 and produced 12 earned runs. Beachy's best performance of the season occurred on July 15 when he struck out 13 of 19 batters against the Huntsville Stars.
Beachy was promoted to the AAA Gwinnett Braves in the fall of 2010. While there, he delivered 2 wins with 0 losses and a 2.17 ERA.
Beachy made his Major League debut with the Braves as the starting pitcher against the Philadelphia Phillies on September 20, 2010, as a replacement for Jair Jurrjens who had injured his knee. Beachy pitched for 4 1⁄3 innings, gave up three runs (one earned), and received his first Major League loss. He had two losses in three starts for the Braves in 2010, with an ERA of 3.00.
On March 24, 2011, the Braves announced that Beachy would be the club's fifth starter for the 2011 season. He was selected over Mike Minor for the final spot in Atlanta's rotation. In his fourth start of the season, he recorded his first major-league win by throwing six scoreless innings against the Los Angeles Dodgers in Dodger Stadium on April 19. During his first game back from an oblique injury, he set a new career high with 11 strikeouts in a game against the Toronto Blue Jays on June 22, 2011. He was 7–3 with a 3.68 ERA in 25 starts that season for the Braves.
Beachy got off to a strong start in 2012, and on May 17, 2012, he threw his first career shutout in a game against the Miami Marlins. He was placed on the disabled list on June 17 after suffering from elbow discomfort and on June 18, he was diagnosed with a partially torn ulnar collateral ligament in his right elbow. At the time, he led all starting pitchers in the Major Leagues with a 2.00 ERA. Beachy underwent Tommy John surgery on June 21, ending his 2012 season.
Beachy began the 2013 season on the 15-day disabled list, still recovering from the surgery and he returned to the Braves' starting rotation and made his season debut on July 29, 2013 in the place of Tim Hudson, who suffered a season-ending ankle fracture. He was 2–1 with a 4.50 ERA in five starts at the end of the season. However, Beachy didn't make the Braves' postseason roster
On December 16, 2013, Beachy agreed with the Braves on a one-year deal for the 2014 season. However, on March 20, it was reported that he would need a second Tommy John surgery and he did not pitch during the 2014 season. Beachy became a free agent on December 2, 2014 after he was non-tendered by the Braves.
On February 21, 2015, Beachy agreed to a 1-year deal with the Los Angeles Dodgers, with a club option for 2016. He returned to the mound in a professional game for the first time since the surgery on June 16, 2015, when he threw 35 pitches for the Rancho Cucamonga Quakes in a California League game. He then pitched in several AAA games for the Oklahoma City Dodgers before he was called up to the majors on July 11. In his first start in two years, Beachy lasted four innings and gave up three runs on five hits. He made a second start on July 20, allowing four runs in five innings, and was then optioned back to AAA. He was designated for assignment on July 30. He made 10 starts in AAA (and one relief appearance) and was 1–1 with a 3.64 ERA.
On January 6, 2016, the Dodgers re-signed Beachy to a one-year, $1.5 million, major league contract. However, on January 27 he was outrighted to the minors. Beachy was invited to major league spring training and emerged as an early favorite to win the fifth starter job to start the season. However, he struggled with his command in spring training action and was sidelined with elbow tendinitis that put him on the minor league disabled list to start the season. After initially thinking it was a minor issue, the tendinitis recurred when he tried to pitch again. and he left the Dodgers spring training complex to return home.
Beachy throws four pitches: a relatively straight four-seam fastball in the 90–94 mph range, a slider (80–84), a changeup (78–82), and a curveball (71–75). Beachy throws mostly fastballs and sliders to right-handed hitters, but he uses his changeup more frequently against left-handed hitters. He is especially fond of using his slider in two-strike counts.
Beachy's parents are Lester and Lori Beachy; he is the eldest of seven siblings.
He majored in pre-law and criminal justice and has worked at a center for delinquent children.