During asymmetric stem cell division, both the daughter stem cell and the presumptive intermediate progenitor cell inherit cytoplasm from their parental stem cell. Thus, proper specification of intermediate progenitor cell identity requires an efficient mechanism to rapidly extinguish the activity of self-renewal factors, but the mechanisms remain unknown in most stem cell lineages. During asymmetric division of a type II neural stem cell (neuroblast) in the Drosophila larval brain, the Brain tumor (Brat) protein segregates unequally into the immature intermediate neural progenitor (INP), where it specifies INP identity by attenuating the function of the self-renewal factor Klumpfuss (Klu), but the mechanisms are not understood. Here, we report that Brat specifies INP identity through its N-terminal B-boxes via a novel mechanism that is independent of asymmetric protein segregation. Brat-mediated specification of INP identity is critically dependent on the function of the Wnt destruction complex, which attenuates the activity of β-catenin/Armadillo (Arm) in immature INPs. Aberrantly increasing Arm activity in immature INPs further exacerbates the defects in the specification of INP identity and enhances the supernumerary neuroblast mutant phenotype in brat mutant brains. By contrast, reducing Arm activity in immature INPs suppresses supernumerary neuroblast formation in brat mutant brains. Finally, reducing Arm activity also strongly suppresses supernumerary neuroblasts induced by overexpression of klu. Thus, the Brat-dependent mechanism extinguishes the function of the selfrenewal factor Klu in the presumptive intermediate progenitor cell by attenuating Arm activity, balancing stem cell maintenance and progenitor cell specification.