ATP-dependent chromatin remodellers modulate nucleosome dynamics by mobilizing or disassembling nucleosomes, as well as altering nucleosome composition. These chromatin remodellers generally function by translocating along nucleosomal DNA at the H3-H4 interface of nucleosomes. Here we show that, unlike other remodellers, INO80 translocates along DNA at the H2A-H2B interface of nucleosomes and persistently displaces DNA from the surface of H2A-H2B. DNA translocation and DNA torsional strain created near the entry site of nucleosomes by INO80 promotes both the mobilization of nucleosomes and the selective exchange of H2A.Z-H2B dimers out of nucleosomes and replacement by H2A-H2B dimers without any additional histone chaperones. We find that INO80 translocates and mobilizes H2A.Z-containing nucleosomes more efficiently than those containing H2A, partially accounting for the preference of INO80 to replace H2A.Z with H2A. Our data suggest that INO80 has a mechanism for dimer exchange that is distinct from other chromatin remodellers including its paralogue SWR1.