The thalassemias are compelling targets for therapeutic genome editing in part because monoallelic correction of a subset of hematopoietic stem cells (HSCs) would be sufficient for enduring disease amelioration. A primary challenge is the development of efficient repair strategies that are effective in HSCs. Here, we demonstrate that allelic disruption of aberrant splice sites, one of the major classes of thalassemia mutations, is a robust approach to restore gene function. We target the IVS1-110G>A mutation using Cas9 ribonucleoprotein (RNP) and the IVS2-654C>T mutation by Cas12a/Cpf1 RNP in primary CD34+ hematopoietic stem and progenitor cells (HSPCs) from β-thalassemia patients. Each of these nuclease complexes achieves high efficiency and penetrance of therapeutic edits. Erythroid progeny of edited patient HSPCs show reversal of aberrant splicing and restoration of β-globin expression. This strategy could enable correction of a substantial fraction of transfusion-dependent β-thalassemia genotypes with currently available gene-editing technology.