SWI/SNF complexes utilize BRG1 (also known as SMARCA4) or BRM (also known as SMARCA2) as alternative catalytic subunits with ATPase activity to remodel chromatin. These chromatin-remodeling complexes are required for mammalian development and are mutated in ~20% of all human primary tumors. Yet our knowledge of their tumor-suppressor mechanism is limited. To investigate the role of SWI/SNF complexes in the DNA-damage response (DDR), we used shRNAs to deplete BRG1 and BRM and then exposed these cells to a panel of 6 genotoxic agents. Compared to controls, the shRNA knockdown cells were hypersensitive to certain genotoxic agents that cause double-strand breaks (DSBs) associated with stalled/collapsed replication forks but not to ionizing radiation-induced DSBs that arise independently of DNA replication. These findings were supported by our analysis of DDR kinases, which demonstrated a more prominent role for SWI/SNF in the activation of the ATR-Chk1 pathway than the ATM-Chk2 pathway. Surprisingly, γH2AX induction was attenuated in shRNA knockdown cells exposed to a topoisomerase II inhibitor (etoposide) but not to other genotoxic agents including IR. However, this finding is compatible with recent studies linking SWI/SNF with TOP2A and TOP2BP1. Depletion of BRG1 and BRM did not result in genomic instability in a tumor-derived cell line but did result in nucleoplasmic bridges in normal human fibroblasts. Taken together, these results suggest that SWI/SNF tumor-suppressor activity involves a role in the DDR to attenuate replicative stress and genomic instability. These results may also help to inform the selection of chemotherapeutics for tumors deficient for SWI/SNF function.