In this study, a polyvinyl alcohol/polyethylene glycol/hydroxypropyltrimethyl ammonium chloride chitosan (PVA/PEG/HACC) ternary composite hydrogel was synthesized using electron-beam radiation. The materials were thoroughly characterized via Fourier transform infrared spectroscopy, X-ray diffraction, scanning electron microscopy, thermogravimetric analysis, Brunauer–Emmett–Teller analysis, gelation fraction tests, and swelling rate tests. Systematic adsorption experiments revealed that the rate of adsorption of calf thymus DNA (ctDNA) by the PVA/PEG/HACC hydrogel reached 89%. The adsorption process followed the Langmuir isotherm and pseudo-second-order kinetic model. This process was mainly characterized by monolayer chemical adsorption, with intraparticle diffusion playing a crucial role. In addition, the process was spontaneous, with higher temperatures enhancing adsorption. The possible adsorption mechanisms included electrostatic interactions, hydrogen bonding, and van der Waals forces. The maximum ctDNA desorption rate was 81.67%. The adsorption rate remained at 71.39% after five adsorption–desorption cycles. The bioactivity of the PVA/PEG/HACC hydrogel was validated by antibacterial, cytotoxicity, and apoptosis tests. The results of this study demonstrated the crucial application potential of adsorbent materials in DNA adsorption and biomedical applications.