Hematopoietic stem cells (HSCs) can both self renew and differentiate into precursors of all types of blood cells. HSCs are divided into an active pool and a quiescent reserve. Cells selected for the active pool contribute to hematopoiesis for many years. Mutations in HSCs can lead to neoplasms such as chronic myeloid leukemia, although the risk of neoplastic HSC disorders varies across mammals. We use allometric scaling relations combined with mutation-selection evolutionary dynamics to determine which mammalian species is most resistant to HSC disorders. We find that the advantage of large mammals at escaping the selective pressure of cancer cells is insufficient to overcome the increased risk of acquiring mutations. Hence, mutation dominates, which favors smaller stem-cell pools and, consequently, smaller mammals, since these minimize the development of mutations in the active stem-cell pool. Consequently, the smaller the active stem-cell pools, the better.