To obtain an efficient dual-drug release and enhance therapeutic efficiency for combination chemotherapy, a glutathione (GSH)-responsive therapeutic amphiphilic polyprodrug copolymer (mPEG-b-PCPT) is synthesized to load doxorubicin (DOX) via hydrophobic and π–π stacking interaction. In this nanomedicine system (mPEG-b-PCPT/DOX), the ratio of the two drugs can be easily modulated by changing the loading content of DOX. The in vitro drug release curves and laser confocal images suggested that the release of CPT and DOX is induced through a “release promotes release strategy”: after internalization into tumor cells, the disulfide bonds in the nanomedicine are cleaved by glutathione (GSH) in the cytoplasm and then lead to the release of CPT. Meanwhile, the disassembly of nanomedicine immediately promotes the co-release of DOX. The optimum dose ratio of CPT and DOX is evaluated via the combination index (CI) value using HepG-2 cells. The results of cell apoptosis and cell viability prove the better synergistic efficiency of the nanomedicine than free drugs at the optimum dose ratio of 1. Consequently, this stimuli-responsive synergistic chemotherapy system provides a direction for the fabrication of nanomedicines possessing promising potential in clinical trials.