Glycopolypeptide-based nanocarriers are an attractive class of drug delivery vehicles because of the involvement of carbohydrates in the receptor-mediated endocytosis process. To enhance their efficacy toward controlled and programmable drug delivery, we have prepared stable glycopolypeptide-based bioactive dual-stimuli-responsive (redox and enzyme) micelles for delivery of anticancer drugs specifically to the cancer cells. The amphiphilic biocompatible miktoarm star copolymer, which comprises two hydrophobic poly(ε-caprolactone) blocks, a short poly(propargyl glycine) middle block, and a hydrophilic galactose glycopolypeptide block, was designed and synthesized. The star copolymer is initially self-assembled into un-cross-linked (UCL) micelles, and free alkyne groups at the core-shell interface of the UCL micelles, which were cross-linked by bis(azidoethyl) disulfide (BADS) via click chemistry to form interface cross-linked (ICL) micelles. ICL micelles were found to be stable against dilution. BADS imparted redox-responsive properties to the micelles, while PCL rendered them enzyme-degradable. Dual-stimuli-responsive release behavior with Dox as model drug was studied individually as well as synergistically by applying two stimuli in different sequences. The galactose-containing UCL and ICL micelles were shown to be nontoxic. Intracellular Dox release from UCL and ICL micelles was demonstrated in liver cancer cells (HepG2) by time-dependent cellular uptake studies, and controlled release from ICL micelles compared to UCL micelles was observed. The present report opens a new approach toward targeted and programmable drug delivery in tumor tissues via a specifically targeted (receptor-mediated), dual-responsive, and stable cross-linked nanocarrier system.