In cancer therapy, it is essential to selectively release cytotoxic agents into the tumor to prevent the adverse effects associated with anticancer drugs. Thus, in this study, a stimuli-sensitive polymer-drug conjugate was synthesized for selective drug release. Doxorubicin (DOX) and docetaxel (DTX) were conjugated onto novel poly(jasmine lactone) based copolymer via a thioketal (TK) linker. In addition, a photosensitizer (chlorin e6) was attached to the polymer, which served as a reactive oxygen species generator to cleave the TK linker. The conjugate is readily self-assembled into micelles less than 100 nm in size. Micelles demonstrate a notable increase in their ability to cause cell death when exposed to near-infrared (NIR) light on MDA-MB-231 breast cancer cells. The increase in cytotoxicity is higher than that observed with the combination of free DOX and DTX. The accumulation of DOX in the nucleus after release from the micelles (laser irradiation) was also confirmed by confocal microscopy. In the absence of light, micelles did not show any toxicity while the free drugs were found toxic irrespective of the light exposure. The obtained results suggest the targeted drug delivery potential of micelles regulated by the external stimuli, i.e., NIR light.