ASXL1 is the obligate regulatory subunit of a deubiquitinase complex whose catalytic subunit is BAP1. Heterozygous mutations of ASXL1 that result in premature truncations are frequent in myeloid leukemias and Bohring–Opitz syndrome. Here we demonstrate that ASXL1 truncations confer enhanced activity on the ASXL1–BAP1 complex. Stable expression of truncated, hyperactive ASXL1–BAP1 complexes in a haematopoietic precursor cell line results in global erasure of H2AK119Ub, striking depletion of H3K27me3, selective upregulation of a subset of genes whose promoters are marked by both H2AK119Ub and H3K4me3, and spontaneous differentiation to the mast cell lineage. These outcomes require the catalytic activity of BAP1, indicating that they are downstream consequences of H2AK119Ub erasure. In bone marrow precursors, expression of truncated ASXL1–BAP1 complex cooperates with TET2 loss-of-function to increase differentiation to the myeloid lineage in vivo. Our data raise the possibility that ASXL1 truncation mutations confer gain-of-function on the ASXL–BAP1 complex.