We numerically and experimentally investigate impact/blast-induced shock mitigation using a quasi-1D woodpile mechanical metamaterial consisting of slender cylindrical rods. In this system, nonlinear stress waves generated by the impact or blast are coupled with local bending vibration modes of the constituent rods. This result in an order of magnitude reduction of transmitted shock without relying on material damping. Specifically, we identify that the arrangement of the local resonances from low to high frequencies enables efficient mitigation of impact/blast energy by splitting strong incident waves into weak ones. We also observe that optimized patterns of the woodpile configurations based on genetic algorithm help making the wave energy equipartition and radiate efficiently in both temporal and spatial domains. This wave attenuation mechanism based on local resonances shows a great potential for the development of nonlinear elastic metamaterials for efficient impact mitigation.