Recent exon-sequencing studies of human tumours have revealed that subunits of BAF (mammalian SWI/SNF) complexes are mutated in more than 20% of all human malignancies, but the mechanisms involved in tumour suppression are unclear. BAF chromatin-remodelling complexes are polymorphic assemblies that use energy provided by ATP hydrolysis to regulate transcription through the control of chromatin structure and the placement of Polycomb repressive complex 2 (PRC2) across the genome. Several proteins dedicated to this multisubunit complex, including BRG1 (also known as SMARCA4) and BAF250a (also known as ARID1A), are mutated at frequencies similar to those of recognized tumour suppressors. In particular, the core ATPase BRG1 is mutated in 5-10% of childhood medulloblastomas and more than 15% of Burkitt's lymphomas. Here we show a previously unknown function of BAF complexes in decatenating newly replicated sister chromatids, a requirement for proper chromosome segregation during mitosis. We find that deletion of Brg1 in mouse cells, as well as the expression of BRG1 point mutants identified in human tumours, leads to anaphase bridge formation (in which sister chromatids are linked by catenated strands of DNA) and a G2/M-phase block characteristic of the decatenation checkpoint. Endogenous BAF complexes interact directly with endogenous topoisomerase IIα (TOP2A) through BAF250a and are required for the binding of TOP2A to approximately 12,000 sites across the genome. Our results demonstrate that TOP2A chromatin binding is dependent on the ATPase activity of BRG1, which is compromised in oncogenic BRG1 mutants. These studies indicate that the ability of TOP2A to prevent DNA entanglement at mitosis requires BAF complexes and suggest that this activity contributes to the role of BAF subunits as tumour suppressors.