Superior flexibility and toughness can be achieved in bioactive hydrogels by the use of a double polymer network with complementary properties. Inspired by this design principle, we here combine polyacrylic acid (PAA) and sodium alginate (SA) to obtain a dual-reinforced double interpenetrating network (d-DIPN) hydrogel. The dual reinforcement involves ionic cross-linking and introduction of SiO nanoparticles, which leads to extraordinary improvements in strength and toughness. Compared with the standard PAA hydrogel that offers an elongation of 240% and a breakage stress of 0.03 MPa, the prepared SA(Ca)-PAA-SiO hydrogel shows an elongation above 1000% and a breakage stress of 1.62 MPa. Moreover, the combination of strong covalent cross-links and weak reversible interactions provides the d-DIPN hydrogel with swelling resistance and self-healing behavior, adhesive abilities, and shape memory performance. Furthermore, we show that the biocompatibility and bone cell proliferation ability of the hydrogels can be improved through a mineralization process despite an observed reduction in breakage strain and stress. Taken as a whole, our work paves the way for the design of strong and tough hydrogels, with potential applications within biomedicine and particularly tissue engineering.