Mutations of ASXL1, encoding a component of the BAP1 histone H2A deubiquitinase complex, occur in human myeloid neoplasms and are uniformly associated with poor prognosis. However, the precise molecular mechanisms through which ASXL1 mutations alter BAP1 activity and drive leukemogenesis remain unclear. Here we demonstrate that cancer-associated frameshift mutations in ASXL1, which were originally proposed to act as destabilizing loss-of-function mutations, in fact encode stable truncated gain-of-function proteins. Truncated ASXL1 increases BAP1 protein stability, enhances BAP1 recruitment to chromatin and promotes the expression of a pro-leukemic transcriptional signature. Through a biochemical screen, we identified BAP1 catalytic inhibitors that inhibit truncated-ASXL1-driven leukemic gene expression and impair tumor progression in vivo. This study represents a breakthrough in our understanding of the molecular mechanisms of ASXL1 mutations in leukemia pathogenesis and identifies small-molecular catalytic inhibitors of BAP1 as a potential targeted therapy for leukemia.