Heiner Mora began his career with Santos de Guápiles. He was a regular starter at rightback for the club before moving to rivals Brujas in 2007. After being seldom used by Brujas, Mora moved to Universidad de Costa Rica and recaptured his previous form. In 2009 he returned to Brujas and became an instant starter for the club. The following season he rejoined Santos de Guápiles and his form drew the attention of top Costa Rican side Saprissa who signed Mora on loan in early 2011. He is rumored to join the Seattle Sounders FC.
Mora has been playing for Norwegian side Hønefoss since 2012. Due to multiple issues, including an inhospitable climate, language barriers, inflexible regulations for immigrants and being separated from his family, he has expressed that he will leave and go back to Costa Rica on May 31, even if it means retiring from professional soccer.