Malignancies arising from mutation of tumor suppressors have unexplained tissue proclivity. For example, BAP1 encodes a widely expressed deubiquitinase for histone H2A, but germline mutations are predominantly associated with uveal melanomas and mesotheliomas. We show that BAP1 inactivation causes apoptosis in mouse embryonic stem cells, fibroblasts, liver, and pancreatic tissue but not in melanocytes and mesothelial cells. Ubiquitin ligase RNF2, which silences genes by monoubiquitinating H2A, promoted apoptosis in BAP1-deficient cells by suppressing expression of the prosurvival genes Bcl2 and Mcl1. In contrast, BAP1 loss in melanocytes had little impact on expression of prosurvival genes, instead inducing Mitf. Thus, BAP1 appears to modulate gene expression by countering H2A ubiquitination, but its loss only promotes tumorigenesis in cells that do not engage an RNF2-dependent apoptotic program.