Stimuli-sensitive polymersomes are one of the important vehicles and have been extensively studied as smart drug delivery system. Polymersomes have added advantage over the micelles because of having the ability to carry not only hydrophobic but also hydrophilic guest in their aqueous core. Among various stimuli, the change of pH and redox reaction is very important for drug delivery purpose especially for anticancer drug. Therefore, in this work, two poly(ethylene glycol) methyl ether methacrylate (mPEG) containing hydrophilic random anionic copolymers, poly[(2-hydroxyethyl methacrylate-3,3'-dithiodipropanoic acid)-co-(poly(ethylene glycol) methyl ether methacrylate)], poly[(HEMA-DTDPA)-co-mPEG] with different copolymer ratios were designed and synthesized. The self-assembly behaviour of these copolymers were studied by use of various techniques, including fluorescence spectroscopy, light scattering, and electron and optical microscopy. Both the copolymers were observed to form negatively charged polymersomes spontaneously in aqueous media at pH 7. The polymersomes were shown to successfully encapsulate hydrophobic as well as hydrophilic guests. The polymersomes of both the polymers showed pH- and redox-sensitive release of encapsulated guest leading to a very good system for cytoplasmic delivery. The polymers were found to be nontoxic and hemocompatible up to a reasonably high concentration. Also the polymers did not show any denaturizing effect on the secondary structure of carrier protein, human serum albumin. It was concluded that these two dual stimuli-sensitive cytocompatible polymersomes can have potential use as drug delivery system in cancer chemotherapy.