The strength and toughness of thermoset epoxy resins are generally mutually exclusive, as are the high performance and rapid recyclability. Experimentally determined mechanical strength values are usually much lower than their theoretical values. The preparation of thermoset epoxy resins with high modulus, high toughness, ultrastrong strength, and highly efficient recyclability is still a challenge. Here, novel hyperbranched epoxy resins (Bn, n = 6, 12, 24)with imide structures by a thiol-ene click reaction. Bn shows an excellent comprehensive function in simultaneously improving the strength, modulus, toughness, low-temperature resistance, and degradability of diglycidyl ether of bisphenol-A (DGEBA). All the mechanical properties first increase and then decrease with minimization of the free volume properties. The improvement is attributable to uniform molecular holes or free volume by a molecular mixture of linear and hyperbranched topological structures. The precise measurement and controllability of the molecular free volume properties of epoxy resins is first discovered, as well as the imide structure degradation of crosslinked epoxy resins. The two conflicts are successfully resolved between strength and toughness and between high performance during service and high efficiency during degradation. These findings provide a route for designing ultrastrong, tough, and recyclable thermoset epoxy resins.