Epoxy composites, as the key insulating materials for high-voltage electrical equipment, operate at high temperature and high mechanical stress for a long period of time, so high-voltage electrical epoxy composites must meet the requirements of high flame retardancy and high mechanical strength at the same time. Although the filling of high proportion of inorganic flame retardant fillers can significantly enhance the flame retardancy of epoxy composites, it can also lead to serious deterioration of the mechanical properties of the composites. This paper is devoted to exploring the mechanical property enhancement method of magnesium hydroxide/epoxy composite flame retardant system by introducing core–shell rubber into the highly filled epoxy composite flame retardant system to toughen it, in order to inhibit the crack extension within the composite material, to reduce the brittleness of the composite material, and to enhance its mechanical strength. The experimental results showed that the mechanical strength of the epoxy composites was enhanced the most when the addition ratio of core–shell rubber reached 20 phr, and its tensile strength reached 39.84 MPa and flexural strength increased to 73.09 MPa, which were increased by 13.2% and 7.6%, respectively, compared with that of the unmodified magnesium hydroxide/epoxy composites. This study also provides a feasible solution for the improvement of mechanical strength of high percentage inorganic flame retardant systems.