Cunniff signed with the Atlanta Braves in June 2013.[2][3] He compiled a 1.99 ERA in 20 appearances at Single–A Lynchburg. The next year, Cunniff made nine more appearances with Lynchburg until a promotion to the Southern League's Mississippi Braves. At the Double–A level, Cunniff pitched in 33 games, recording a 2.05 ERA.[1]
The Braves added Cunniff to the team's 40-man roster on November 19, 2014.[4] He was invited to spring training in 2015, and sent to the minors as one of the final cuts. After Craig Kimbrel and Melvin Upton, Jr. were traded to the San Diego Padres on April 6, Cunniff was called up.[5] Cunniff went on the disabled list for the first time in his career on June 26, 2015, after suffering a groin strain.[6] He was designated for assignment on December 18, 2015.[7]
Due to a loss of effectiveness arising from a heavy workload in his first Major League Baseball season, Cunniff was not invited to spring training in 2016. Instead, he began the season with the Gwinnett Braves. After two months, Cunniff was demoted to Mississippi, and later called up on August 3 from the Triple–A level.[8] Cunniff was optioned back to Gwinnett on August 12.[9] He spent the rest of August between the major and minor league levels.[10][11] He was outrighted on November 2, 2016. He elected free agency five days later on November 7.[12]
On January 18, 2017, Cunniff signed a minor league contract with the Miami Marlins organization.[13] On April 14, while pitching for the Triple-A New Orleans Baby Cakes, Cunniff pitched the ninth inning of a combined no-hitter against the Iowa Cubs, with Scott Copeland pitching the first 7 innings and Hunter Cervenka taking care of the eighth.[14] In 36 games for New Orleans, he posted a 4.45 ERA with 54 strikeouts and 3 saves in 54+2⁄3 innings pitched. He elected free agency following the season on November 6.[15]
On April 5, 2018, Cunniff signed with the Bravos de León of the Mexican League. He was released on July 3, 2018. In 15 games of relief 14.2 innings he went 0-1 with a 2.45 era and 10 strikeouts.
On July 14, 2018, Cunniff signed with the New Britain Bees of the Atlantic League. He became a free agent following the 2018 season. In 26 games of relief 28 innings he went 2-0 with a 3.54 era and 25 strikeouts
On February 19, 2019, Cunniff signed with the Tigres de Quintana Roo of the Mexican League. He was released on April 25, 2019. In 7 games 6.2 innings of relief he struggled mightily going 0-2 with a 10.80 era and 6 strikeouts.
On May 17, 2019, Cunniff signed with the Olmecas de Tabasco of the Mexican League. He was released on July 16, 2019. In 19 games 23.1 innings of relief he went 1-3 with a 4.63 era and 17 strikeouts.
On January 21, 2022, Cunniff signed with the Lincoln Saltdogs of the American Association.[16] In 2022, Cunniff recorded a 1–1 record and 5.11 ERA in 11 appearances with the Saltdogs. On June 16, 2022, Cunniff was released by the Saltdogs.
