This paper focusses on the load-sustaining and transfer mechanisms of sandwich beams with various types of PMI foam cores under low-velocity impact loading. In the case of quasi-static loading, the different failure modes, failure loads, and deflections were obtained, which agreed well with the results predicted by the theory of sandwich structure. In the case of impact loading, the clamped sandwich beams were subjected to the impact of a striker bar with a momentum of 10 kg∙m/s to 20 kg∙m/s. The de-acceleration of the strike bar was measured to analyze the impact force and energy absorption, and the corresponding failure modes were also obtained. The results showed that the impact force and the corresponding duration time increases with the increases in the thickness of the face sheet and the density of the core. In addition, the failure modes of the sandwich beams transferred from the shear failure mode to the tensile failure mode, which was attributed to the strength ratio between the bottom face sheet and the core. In combination with the experimental results and the plastic hinge theory, the deformation mechanisms of the different sandwich beams are also discussed.