Ubiquitin chain complexity in cells is likely regulated by a diverse set of deubiquitinating enzymes (DUBs) with distinct ubiquitin chain preferences. Here we show that the polyglutamine disease protein, ataxin-3, binds and cleaves ubiquitin chains in a manner suggesting that it functions as a mixed linkage, chain-editing enzyme. Ataxin-3 cleaves ubiquitin chains through its amino-terminal Josephin domain and binds ubiquitin chains through a carboxyl-terminal cluster of ubiquitin interaction motifs neighboring the pathogenic polyglutamine tract. Ataxin-3 binds both Lys(48)- or Lys(63)-linked chains yet preferentially cleaves Lys(63) linkages. Ataxin-3 shows even greater activity toward mixed linkage polyubiquitin, cleaving Lys(63) linkages in chains that contain both Lys(48) and Lys(63) linkages. The ubiquitin interaction motifs regulate the specificity of this activity by restricting what can be cleaved by the protease domain, demonstrating that linkage specificity can be determined by elements outside the catalytic domain of a DUB. These findings establish ataxin-3 as a novel DUB that edits topologically complex chains.