Inactivation of ARID1A and other components of the nuclear SWI/SNF protein complex occurs at very high frequencies in a variety of human malignancies, suggesting a widespread role for the SWI/SNF complex in tumour suppression1. However, the underlying mechanisms remain poorly understood. Here we show that ARID1A-containing SWI/SNF complex (ARID1A-SWI/SNF) operates as an inhibitor of the pro-oncogenic transcriptional coactivators YAP and TAZ2. Using a combination of gain- and loss-of-function approaches in several cellular contexts, we show that YAP/TAZ are necessary to induce the effects of the inactivation of the SWI/SNF complex, such as cell proliferation, acquisition of stem cell-like traits and liver tumorigenesis. We found that YAP/TAZ form a complex with SWI/SNF; this interaction is mediated by ARID1A and is alternative to the association of YAP/TAZ with the DNA-binding platform TEAD. Cellular mechanotransduction regulates the association between ARID1A-SWI/SNF and YAP/TAZ. The inhibitory interaction of ARID1A-SWI/SNF and YAP/TAZ is predominant in cells that experience low mechanical signalling, in which loss of ARID1A rescues the association between YAP/TAZ and TEAD. At high mechanical stress, nuclear F-actin binds to ARID1A-SWI/SNF, thereby preventing the formation of the ARID1A-SWI/SNF-YAP/TAZ complex, in favour of an association between TEAD and YAP/TAZ. We propose that a dual requirement must be met to fully enable the YAP/TAZ responses: promotion of nuclear accumulation of YAP/TAZ, for example, by loss of Hippo signalling, and inhibition of ARID1A-SWI/SNF, which can occur either through genetic inactivation or because of increased cell mechanics. This study offers a molecular framework in which mechanical signals that emerge at the tissue level together with genetic lesions activate YAP/TAZ to induce cell plasticity and tumorigenesis.