Disulfide bonds are commonly exploited as dynamic crosslinks to fabricate degradable self-healing hydrogels. However, the low energy dissipation capability and low density of disulfide crosslinks in the hydrogel networks give these hydrogels poor mechanical properties, slow and non-autonomous self-healing, and incomplete polymer degradation. This paper reports a strategy for synthesizing multifunctional hydrogels by copolymerizing 2,3-dimercapto-1-propanol and meso-2,3-dimercaptosuccinic acid, yielding a dynamic poly(disulfide) backbone and numerous rapidly reversible physical crosslinks (H-bonds and ionic interactions). The high-density disulfide bonds and multiphysical crosslinkers synergistically provide the hydrogels with extremely fast self-healing in air and underwater, extraordinary stretchability, and complete and fast degradability. The hydrogels show various functionalities including three-dimensional printability in air and underwater, good electrical conductivity, non-cytotoxicity and bio-tissue adhesion. This strategy opens a new route for exploiting degradable self-healing multifunctional hydrogels with extraordinary features for biomedical and engineering applications.