Mussel-inspired hydrogels have gained attention for underwater applications, including treatment of wastewater. However, they are typically limited by poor mechanical properties, short-term mechanical stability and by not being reusable. Here, we develop a mechanically stable and self-healing hydrogel with high mechanical strength for the degradation of dyes in wastewater, based on cellulose-derived co-polydopamine@Pd nanoparticles. A dynamic catechol redox system was achieved by reversible conversion between semiquinone and quinone/hydroquinone radicals, endowing the hydrogel with stable mechanical properties and self-healing behavior. Furthermore, a graphene oxide membrane is covalently grafted on to the hydrogel surface, which regulates its water permeability and intercepts some metal ions or large particles, protecting the hydrogel structure. High catalytic activity for anionic and cationic dyes is achieved, with the degradation rate reaching more than 95% after multiple cycles without significant deterioration in performance or hydrogel structure. Our work demonstrates a route to achieve mechanically stable hydrogels for degradation of organic dyes in wastewater.