It is of great significance to investigate the dynamic responses of functionally graded materials (FGMs). A series of experiments are conducted to evaluate the dynamic behaviors of the laminated and graded ZrC-Mo composites with three graded exponents (i.e., 0.69, 1.35, and 2.70) by the split Hopkinson pressure bar (SHPB) device. The graded composites with an exponent of 0.69 show the highest strength and best performances of the three. It results from the formation of local stress-transferring structures and the interaction of the ZrC component and Mo component. Based on the digital imaging correlation (DIC) method, different evolutions of local strains in the ZrC-rich and the Mo-rich regions are analyzed by changing the gradient directions of the composites. The transmission behaviors of stress waves in the laminated and graded composite with multi-interfaces are investigated theoretically. The finite element method (FEM) is used to evaluate influences of the plasticity of metal component, and the transmitted coefficient in theory is employed to optimize and evaluate the laminated and graded structures. It also indicates the special role of loading frequency. These results might be helpful for a profound understanding of the internal wave propagation and guide the structural designing optimization.