The continuous carbon-fiber-reinforced magnesium matrix composite (C_f/Mg) is a new type of composite material made of a magnesium alloy sheet and carbon-fiber-reinforced composite material with alternating layers. It has the advantages of high damage tolerance, light weight, and corrosion resistance, and has become the first choice of lightweight materials in aerospace, transportation, and other fields. Because impact-resistance serves as an important index for its structural design and performance stability, a continuous carbon-fiber-reinforced magnesium matrix composite with indirect bonding using a modified epoxy resin was designed in this study. Moreover, C_f/Mg was chosen to be the object of research through the selection of constituent materials such as magnesium alloys, carbon fibers, resins, and other properties, which matched the aim of realizing a lightweight material. With the help of hot-compression molding technology, dynamic impact mechanical behavior, and damage analysis technology, the structural design and preparation process optimization of epoxy resin carbon-fiber prepregs and magnesium alloy layer materials, as well as the dynamic impact mechanical response characteristics and damage evolution process under different impact energy conditions, were studied. Accordingly, through a combination of low-velocity impact experiments and numerical simulations, the effects of continuous multiple impacts at the same location with the same impact energy, as well as impacts with the same impact energy and different punch diameters, on the low-velocity impact damage behavior and dynamic impact response characteristics of C_f/Mg were investigated. The results of this study show that when the 5J impact is applied four times consecutively, the peak impact load gradually increases with the increasing number of impacts. Moreover, the peak impact loads of the second, third, and fourth impacts increase by 6.09%, 10.7%, and 14.5%, respectively, compared with the results of the first impact.