Rubber cement-based material is one of the important ways of utilizing waste rubber. Fatigue failure and impact failure are the most common failure forms of concrete structures, but the low stiffness and low strength of rubber cement-based materials do no allow them to be used in the main bearing structure. Therefore, the use of appropriate reinforcement materials and technical methods to effectively improve the yield stiffness, bearing capacity, ductility, and energy dissipation capacity of rubber cement-based materials can not be ignored. To explore the dynamic response characteristics of rubber cement mortar (RCM) with different confine conditions, the split Hopkinson pressure bar (SHPB) cyclic impact tests of four kinds of confined RCM were carried out. Firstly, the four different confine modes of RCM were designed by using the carbon fiber reinforced polymer (CFRP) sheet and steel cylinder. Then, the SHPB test system was used to carry out the amplitude-enhanced cyclic impact tests of RCM with different confine modes. Lastly, the dynamic mechanical behavior, energy behavior, dynamic damage, and failure modes of RCM with different confine modes were compared and analysed. The results show that the end faces and side of RCM were confined effectively by using the CFRP sheet and steel cylinder, which strengthened the structural resistance of RCM. However, with the simultaneous increase in impact load and impact times, stiffness degradation still occurred due to the cumulative effect of fatigue damage. The end friction constraint of the CFRP sheet and the passive confining pressure constraint of the CFRP sheet/steel cylinder significantly improved the energy dissipation capacity and impact resistance of RCM, controlled and delayed the transverse expansion deformation and crack development of RCM, and ensured the minimum damage of RCM structure. The purpose of this paper is to provide a reference for further promoting the resource utilization of waste rubber and the practical engineering application of rubber cement-based materials.