Air-blast loading is a serious threat to military and civil vehicles, buildings, containers, and cargo. Applications of sandwich-structured composites have attracted increasing interest in modern lightweight design and in the construction of dynamic loading regimes due to their high resistance against blast and ballistic impacts. The functional properties of such composites are determined by the interplay of their face sheet material and the employed core topology. The core topology is the most important parameter affecting the structural behavior of sandwich composites. Therefore, this contribution presents a thorough numerical investigation of different core topologies in sandwich-structured composites subjected to blast loading. Special emphasis is put on prismatic and lattice core topologies displaying auxetic and classical non-auxetic deformation characteristics in order to illustrate the beneficial properties of auxetic core topologies. Their dynamic responses, elastic and plastic deformations, failure mechanisms, and energy absorption capabilities are numerically analyzed and compared. The numerical studies are performed by means of the commercial finite element code ABAQUS/Explicit, including a model for structural failure.