To address the need for rapid in situ plugging and repair of hydraulic machinery and chemical pipelines and to resolve the issue that a single curing agent cannot simultaneously achieve rapid curing and excellent mechanical properties in epoxy resin systems, this study explores the use of composite curing agents. In particular, effective formulations are designed for mixing fast and slow curing agents, studying their effects on the curing behavior, curing quality, and mechanical properties of epoxy resins and elucidating their influence mechanisms. The results indicate that three resin systems meet the requirements for rapid curing (curing time within 30 min): 4A6B/EP, 2A8B/EP, and 0A10B/EP. Among them, 4A6B/EP exhibits the best curing quality and mechanical properties. In particular, 4A6B/EP demonstrates the lowest values of curing shrinkage rate, internal curing stress, average pore size, porosity, and cumulative pore volume. Its low internal stress and low defects reduce the stress concentration, while more efficient deflection and branching of internal cracks enhance its deformation resistance. Consequently, 4A6B/EP shows the highest microhardness, fracture toughness, tensile strength, Young’s modulus, and elongation after fracture. Based on the comprehensive evaluation of rapid curing characteristics and mechanical properties, the 4A6B/EP system offers the best overall performance. Therefore, it is recommended as the preferred resin system for rapid plugging and repair of composite materials, providing a theoretical basis and technical support for boosting the application of epoxy resin composite materials in high-tech fields.