Aliphatic polyesters are intrinsically enzymatic-biodegradable, and there is ever-increasing demand for safe and smart nextgeneration biomaterials including drug delivery nano-vectors in cancer research. Using bioresource-based biodegradable polyesters is one of the elegant strategies to meet this requirement; here, we report an Lamino acid-based amide-functionalized polyester platform and explore their lysosomal enzymatic biodegradation aspects to administrate anticancer drugs in cancer cells. L-Aspartic acid was chosen and different amide-side chain-functionalized di-ester monomers were tailor-made having aromatic, aliphatic, and bio-source pendant units. Under solvent-free melt polycondensation methodology; these monomers underwent polymerization to yield high molecular weight polyesters with tunable thermal properties. PEGylated L-aspartic monomer was designed to make thermo-responsive amphiphilic polyesters. This amphiphilic polyester was self-assembled into a 140 ± 10 nm-sized spherical nanoparticle in aqueous medium, which exhibited lower critical solution temperature at 40−42 °C. The polyester nano-assemblies showed excellent encapsulation capabilities for anticancer drug doxorubicin (DOX), anti-inflammatory drug curcumin, biomarkers such as rose bengal (RB), and 8-hydroxypyrene-1,3,6-trisulfonic acid trisodium salt. The amphiphilic polyester NP was found to be very stable under extracellular conditions and underwent degradation upon exposure to horse liver esterase enzyme in phosphate-buffered saline at 37 °C to release 90% of the loaded cargoes. Cytotoxicity studies in breast cancer MCF 7 and wild-type mouse embryonic fibroblasts cell lines revealed that the amphiphilic polyester was non-toxic to cell lines up to 100 μg/mL, while their drug-loaded polyester nanoparticles were able to inhibit the cancerous cell growth. Temperature-dependent cellular uptake studies further confirmed the energy-dependent endocytosis of polymer NPs across the cellular membranes. Confocal laser scanning microscopy assisted time-dependent cellular uptake analysis directly evident for the endocytosis of DOX loaded polymer NP and their internalization for biodegradation. In a nutshell, the present investigation opens up an avenue for the L-amino acid-based biodegradable polyesters from L-aspartic acids, and the proof of concept is demonstrated for drug delivery in the cancer cell line.