In this article, a novel meta-lattice sandwich structure is proposed and designed for impulsive wave attenuation and dynamic load mitigation. This original meta-lattice truss core sandwich structure has a similar configuration as a normal lattice sandwich structure, except that its truss bars are composed of meta-lattice truss unit cells. The design philosophy of locally resonant elastic metamaterials is integrated into the meta-lattice truss unit cell whereby a relatively heavier metal core (the resonator) is coated with a soft material layer (rubber coat), which is then connected to an outer shell. Based on this unique construction, several frequency band gaps are created by the locally resonant behavior of the specially designed resonators, in which stress waves within the stopping band gaps are not able to propagate through the material. Analytical spring-mass model is employed to predict the frequency band gaps, whereas numerical finite element simulation is utilized to model the continuum structure under impulsive loadings. The impact response, wave attenuation, and stress distribution contours between normal sandwich structure and meta-lattice sandwich structure are compared and analyzed. The mechanisms of wave mitigation and energy absorption by the internal resonators are thoroughly investigated. Results evidently show that the proposed meta-lattice sandwich structure has a more superior ability for impact mitigation and higher kinetic energy absorption capability due to the locally resonant behavior of the internal resonators.