The loss of a tumour suppressor is known to lead to malignancy in specific tissues. However, the mechanisms driving this tissue specificity are not well understood. For example, BAP1, is a powerful tumour suppressor encoding a widely expressed deubiquitinase. And yet, individuals with heterozygous BAP1 loss are predisposed predominantly to just two cancers: uveal melanoma and mesotheliomas. Using a multi-omic approach, we identified a ubiquitin ligase (RNF2) that functions in coordination with BAP1 to find-tune activity of histone H2A. We found that in many cell types, BAP1 inactivation induces cell death through suppression of anti-apoptotic factors Bcl1 and Mcl1. However, in melanocytes and mesothelial cells, the loss of BAP1 instead induces cell proliferation and migration.