In this paper, the influence of different fiber materials on the dynamic splitting mechanical properties of concrete was investigated. Brazil disc dynamic splitting tests were conducted on plain concrete, palm fiber-reinforced concrete, and steel fiber-reinforced concrete specimens using a split Hopkinson pressure bar (SHPB) test device with a 100 mm diameter and a V2512 high-speed digital camera. The Digital Image Correlation (DIC) technique was used to analyze the fracture process and crack propagation behavior of different fiber-reinforced concrete specimens and obtain their dynamic tensile properties and energy dissipation. The experimental results indicate that the addition of fibers can enhance the impact toughness of concrete, reduce the occurrence of failure at the loading end of specimens due to stress concentration, delay the time to failure of specimens, and effectively suppress the expansion of cracks. Steel fibers exhibit a better crack-inhibiting effect on concrete compared to palm fibers. The incident energy for the three types of concrete specimens is roughly the same under the same impact pressure. Compared with plain concrete, the energy absorption rate of palm fiber concrete is decreased, while that of steel fiber concrete is increased. Palm fiber-reinforced concrete and steel fiber-reinforced concrete have lower peak strains than plain concrete under the same loading duration. The addition of steel fibers significantly impedes the internal cracking process of concrete specimens, resulting in a relatively slow growth of damage variables.