Dasatinib and Venetoclax in Treating Patients With Philadelphia Chromosome Positive or BCR-ABL1 Positive Early Chronic Phase Chronic Myelogenous Leukemia

This phase II trial studies how well dasatinib and venetoclax work in treating patients with Philadelphia chromosome positive or BCR-ABL1 positive early chronic phase chronic myelogenous leukemia. Dasatinib and venetoclax may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth.

Inclusion Criteria: * Diagnosis of Ph-positive or BCR-ABL positive CML in early chronic phase CML (i.e., time from diagnosis ≤ 12 months). Except for hydroxyurea and/or 1 to 2 doses of cytarabine patients must have received no or minimal prior therapy, defined as \ 12 months), accelerated or blast phase are excluded; the definitions of CML phases are as follows: * Early chronic phase: * Time from diagnosis to therapy ≤12 months * Late chronic phase: * Time from diagnosis to therapy \> 12 months * Blastic phase: * Presence of 30% blasts or more in the peripheral blood or bone marrow * Accelerated phase CML: * Presence of any of the following features: * Peripheral or marrow blasts 15% or more * Peripheral or marrow basophils 20% or more * Thrombocytopenia \< 100 x 10\^9/L unrelated to therapy * Documented extramedullary blastic disease outside liver or spleen