Current methodologies for targeting the mitochondrial genome for research and/or therapy development in mitochondrial diseases are restricted by practical limitations and technical inflexibility. A molecular toolbox for CRISPR-mediated mitochondrial genome editing is desirable, as this could enable targeting of mtDNA haplotypes using the precision and tuneability of CRISPR enzymes. “MitoCRISPR” systems described to date lack reproducibility and independent corroboration. We have explored the requirements for MitoCRISPR in human cells by CRISPR nuclease engineering, including the use of alternative mitochondrial protein targeting sequences and smaller paralogues, and the application of gRNA modifications for mitochondrial import. We demonstrate varied mitochondrial targeting efficiencies and effects on mitochondrial dynamics/function of different CRISPR nucleases, with Lachnospiraceae bacterium ND2006 (Lb) Cas12a being better targeted and tolerated than Cas9 variants. We also provide evidence of Cas9 gRNA association with mitochondria in HeLa cells and isolated yeast mitochondria, even in the absence of a targeting RNA aptamer. Our data link mitochondrial-targeted LbCas12a/crRNA with increased mtDNA copy number dependent upon DNA binding and cleavage activity. We discuss reproducibility issues and the future steps necessary for MitoCRISPR.