Mitochondrial AAA+ quality control proteases regulate diverse aspects of mitochondrial biology through specialized protein degradation, but the underlying molecular mechanisms that define the diverse activities of these enzymes remain poorly defined. The mitochondrial AAA+ protease AFG3L2 is of particular interest, as genetic mutations localized throughout AFG3L2 are linked to diverse neurodegenerative disorders. However, a lack of structural data has limited our understanding of how mutations impact enzymatic activity. Here, we used cryo-EM to determine a substrate-bound structure of the catalytic core of human AFG3L2. This structure identifies multiple specialized structural features within AFG3L2 that integrate with conserved structural motifs required for hand-over-hand ATP-dependent substrate translocation to engage, unfold and degrade targeted proteins. Mapping disease-relevant AFG3L2 mutations onto our structure demonstrates that many of these mutations localize to these unique structural features of AFG3L2 and distinctly influence its activity and stability. Our results provide a molecular basis for neurological phenotypes associated with different AFG3L2 mutations, and establish a structural framework to understand how different members of the AAA+ superfamily achieve specialized, diverse biological functions.