Career
He previously played for the San Diego Padres. Despaigne played for the Industriales of the Cuban National Series, making his debut in the league in 2007. He played for the Cuban national baseball team, and defected from Cuba while in Europe for the 2013 World Portuguese Tournament.
Despaigne became a legal resident of Spain, and traveled to Mexico.
San Diego Padres
Despaigne and fellow Cuban defector Aledmys Díaz held a showcase for Major League Baseball teams on February 13, 2014. Despaigne signed a minor league deal with the San Diego Padres on May 2, 2014.
The Padres assigned Despaigne to the San Antonio Missions of the Double-A Texas League, where in two games started, he allowed one earned run in 7 2⁄3 innings pitched. The Padres promoted Despaigne to the El Paso Chihuahuas of the Triple-A Pacific Coast League on May 26.
Despaigne was called up by the Padres on June 23 to start that night against the San Francisco Giants.
Despaigne pitched seven shutout innings, allowing four hits in his major league debut. In his fifth major league start on July 20, Despaigne pitched 7 2/3 no-hit innings before the New York Mets" Daniel Murphy doubled. Baltimore Orioles
On February 4, 2016, Despaigne was traded to the Baltimore Orioles for minor league pitcher Jean Cosme.