Mutations of the mitochondrial genome (mtDNA) underlie a substantial portion of mitochondrial disease burden. These disorders are currently incurable and effectively untreatable, with heterogeneous penetrance, presentation and prognosis. To address the lack of effective treatment for these disorders, we exploited a recently developed mouse model that recapitulates common molecular features of heteroplasmic mtDNA disease in cardiac tissue: the m.5024C>T tRNAAla mouse. Through application of a programmable nuclease therapy approach, using systemically administered, mitochondrially targeted zinc-finger nucleases (mtZFN) delivered by adeno-associated virus, we induced specific elimination of mutant mtDNA across the heart, coupled to a reversion of molecular and biochemical phenotypes. These findings constitute proof of principle that mtDNA heteroplasmy correction using programmable nucleases could provide a therapeutic route for heteroplasmic mitochondrial diseases of diverse genetic origin.