Current methodologies for targeting the mitochondrial genome for basic research and/or therapeutic strategy development in mitochondrial diseases are restricted by practical limitations and technical inflexibility. The development of a functional molecular toolbox for CRISPR-mediated mitochondrial genome editing is therefore desirable, as this could enable precise targeting of mtDNA haplotypes using the precision and tuneability of CRISPR enzymes; however, published reports of MitoCRISPR systems have, to date, lacked reproducibility and independent corroboration. Here, we have explored the requirements for a functional MitoCRISPR system in human cells by engineering several versions of CRISPR nucleases, including the use of alternative mitochondrial protein targeting sequences and smaller paralogues, and the application of gRNA modifications that reportedly induce mitochondrial import. We demonstrate varied mitochondrial targeting efficiencies and influences 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. Finally, we present evidence linking 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 if MitoCRISPR is to be realised.