A novel dual-stimuli cleavable linker containing adjacent UV light-sensitive o-nitrobenzyl ester and GSH-responsive disulfide bonds was first designed and synthesized to increase the responsivity to external stimuli. The functionalized linker was then utilized to prepare a dual-responsive amphiphilic block copolymer using ring-opening polymerization and atom transfer radical polymerization. The copolymer formed a micelle in an aqueous solution and showed dual-stimuli responses including photo-mediated cleavage under UV light irradiation at 365 nm as well as reduction-responsive degradation in the presence of a reducing agent. The micelle was nontoxic against three cell lines and majorly internalized via clathrin-mediated endocytosis. Doxorubicin (Dox) was loaded in the hydrophobic core of the micelle. Enhancement of a cell-killing effect against A549 cells was clearly observed in the Dox-encapsulated micelle when exposed to UV light.