Jose Mesa Jr. is the son of major leaguer Jose Mesa, who played with various clubs (Baltimore Orioles, Cleveland Indians, San Francisco Giants, Seattle Mariners, Philadelphia Phillies, Pittsburgh Pirates, Colorado Rockies, Detroit Tigers) from 1987 through 2007. His father was also a pitcher. Mesa Jr. was committed to play baseball at Seminole State College of Florida but was drafted by the New York Yankees out of Charles Flanagan high school in Pembroke Pines, Florida and he opted to sign with the Yankees and start his Major League Baseball career instead. He was drafted in the 24th round of the 2012 MLB June Amateur Draft and he did not make it to rookie ball until the 2014 season. In his first season as a professional in 2014, he went 2-0 with a 2.79 ERA and in nine game appearances. The highest he made it was Double-A. Mesa Jr. was claimed off of waivers by the Batimore Orioles. He returned to the Yankees in 2018 after he was designated for assignment by the Orioles.