Dual responsive polymer nanoscaffolds for administering anticancer drugs both at the tumor site and intracellular compartments are made for improving treatment in cancers. The present work reports the design and development of new thermo- and enzyme-responsive amphiphilic copolymer core-shell nanoparticles for doxorubicin delivery at extracellular and intracellular compartments, respectively. A hydrophobic acrylate monomer was tailor-made from 3-pentadecylphenol (PDP, a natural resource) and copolymerized with oligoethylene glycol acrylate (as a hydrophilic monomer) to make new classes of thermo and enzyme dual responsive polymeric amphiphiles. Both radical and reversible addition-fragmentation chain transfer (RAFT) methodologies were adapted for making the amphiphilic copolymers. These amphiphilic copolymers were self-assembled to produce spherical core-shell nanoparticles in water. Upon heating, the core-shell nanoparticles underwent segregation to produce larger sized aggregates above the lower critical solution temperature (LCST). The dual responsive polymer scaffold was found to be capable of loading water insoluble drug, such as doxorubicin (DOX), and fluorescent probe-like Nile Red. The drug release kinetics revealed that DOX was preserved in the core-shell assemblies at normal body temperature (below LCST, ≤ 37 °C). At closer to cancer tissue temperature (above LCST, ∼43 °C), the polymeric scaffold underwent burst release to deliver 90% of loaded drugs within 2 h. At the intracellular environment (pH 7.4, 37 °C) in the presence of esterase enzyme, the amphiphilic copolymer ruptured in a slow and controlled manner to release >95% of the drugs in 12 h. Thus, both burst release of cargo at the tumor microenvironment and control delivery at intracellular compartments were accomplished in a single polymer scaffold. Cytotoxicity assays of the nascent and DOX-loaded polymer were carried out in breast cancer (MCF-7) and cervical cancer (HeLa) cells. Among the two cell lines, the DOX-loaded polymers showed enhanced killing in breast cancer cells. Furthermore, the cellular uptake of the DOX was studied by confocal and fluorescence microscopes. The present investigation opens a new enzyme and thermal-responsive polymer scaffold approach for DOX delivery in cancer cells.