Pendent functionalization of biodegradable polymers provides unique importance in biological applications. In this work, we have synthesized a polymeric nanocarrier for the controlled release of the anticancer drug doxorubicin (DOXI). Inspired by the pH responsiveness of acylhydrazine bonds along with the interesting self-assembly behavior of amphiphilic copolymers, this report delineates the development of a PEG-SS-PCL-DOXI copolymer consisting of DOXI, PEG, and a caprolactone backbone. First, the inclusion of a PEG moiety in the copolymer helps to achieve biocompatibility and aqueous solubility as well as a prolonged circulation time of the nanocarrier. Second, an acid-sensitive acylhydrazine-based linkage is chosen to attach DOXI to trigger sustained drug release, whereas the inclusion of an enzymatically cleavable disulfide linkage in the backbone adds to the advantage of backbone biodegradability at the intracellular level.