Malignant mesothelioma (MM) is poorly responsive to systemic cytotoxic chemotherapy and invariably fatal. Here we describe a screen of 94 drugs in 15 exome-sequenced MM lines and the discovery of a subset defined by loss of function of the nuclear deubiquitinase BRCA associated protein-1 (BAP1) that demonstrate heightened sensitivity to TRAIL (tumour necrosis factor-related apoptosis-inducing ligand). This association is observed across human early passage MM cultures, mouse xenografts and human tumour explants. We demonstrate that BAP1 deubiquitinase activity and its association with ASXL1 to form the Polycomb repressive deubiquitinase complex (PR-DUB) impacts TRAIL sensitivity implicating transcriptional modulation as an underlying mechanism. Death receptor agonists are well-tolerated anti-cancer agents demonstrating limited therapeutic benefit in trials without a targeting biomarker. We identify BAP1 loss-of-function mutations, which are frequent in MM, as a potential genomic stratification tool for TRAIL sensitivity with immediate and actionable therapeutic implications.