The emergence of treatment resistance significantly reduces the clinical utility of many effective targeted therapies. Although both genetic and epigenetic mechanisms of drug resistance have been reported, whether these mechanisms are stochastically selected in individual tumors or governed by a predictable underlying principle is unknown. Here, we report that the dependence of cancer stem cells (CSCs), not bulk tumor cells, on the targeted pathway determines the molecular mechanism of resistance in individual tumors. Using both spontaneous and transplantable mouse models of sonic hedgehog (SHH) medulloblastoma (MB) treated with an SHH/Smoothened inhibitor, sonidegib/LDE225, we show that genetic-based resistance occurs only in tumors that contain SHH-dependent CSCs (SD-CSCs). In contrast, SHH MBs containing SHH-dependent bulk tumor cells but SHH-independent CSCs (SI-CSCs) acquire resistance through epigenetic reprogramming. Mechanistically, elevated proteasome activity in SMOi-resistant SI-CSC MBs alters the tumor cell maturation trajectory through enhanced degradation of specific epigenetic regulators, including histone acetylation machinery components, resulting in global reductions in H3K9Ac, H3K14Ac, H3K56Ac, H4K5Ac, and H4K8Ac marks and gene expression changes. These results provide new insights into how selective pressure on distinct tumor cell populations contributes to different mechanisms of resistance to targeted therapies. This insight provides a new conceptual framework to understand responses and resistance to SMOis and other targeted therapies.