The development of copolymerization techniques that can randomly incorporate biodegradable moieties into the hyperbranched polyglycerol backbone is an option to prevent its bioaccumulation in vivo. In this study, redox-responsive and biocompatible hyperbranched polyglycerol copolymers of glycidol and 1,4,5-oxadithiepan-2-one were synthesized with an adjustable molecular weight and a defined disulfide bond content through anionic and coordination–insertion ring-opening polymerization. A truly random incorporation of the monomers was achieved under both copolymerization mechanisms. The copolymers were further characterized in terms of their aggregation behavior in solution, degradability, in vitro cell viability, and blood compatibility for potential future biomedical applications. Transmission electron microscopy revealed that the copolymer assembled into nanoparticles with a size range of 20 nm. The copolymers underwent degradation when incubated with two different reducing agents, resulting in smaller fragments of the polymer with thiol end groups. The copolymers demonstrated good biocompatibility, making them suitable for further investigation in biomedical applications.