Of the eight distinct polyubiquitin chains that can be assembled, K48-linked ubiquitin is the most well-understood linkage and modification of proteins with K48 chains targets the modified protein for degradation. By removing ubiquitin from substrates or trimming ubiquitin chains, deubiquitinases (DUBs) can modulate the outcome of ubiquitylation. MINDY1 and MINDY2 are members of the MINDY family of DUBs that have exquisite specificity for cleaving K48-linked polyubiquitin. Being recently discovered DUBs, we have a poor understanding of their catalytic mechanism. By analysing crystal structures of MINDY1 alone and in complex with monoubiquitin or K48-linked ubiquitin chains, we here reveal how substrate interaction relieves autoinhibition and activates the DUB. Further, our analyses reveal a non-canonical catalytic triad composed of Cys-His-Thr and explain how these DUBs sense both ubiquitin chain length and linkage type to trim K48-linked ubiquitin chains. Our findings highlight the multiple layers of regulation modulating DUB activity in MINDY1 and MINDY2.