In this study, a truncated origami structure, originated from the Miura-ori structure, was designed. The compressive behaviors of this structure subjected to x2-direction (in-plane) and x3-direction (out-of-plane) compression were studied both experimentally and numerically. The structure with a smaller truncated ratio value, e, was more similar to a dense solid. Representative specimens of the Miura-ori and the truncated origami designs were fabricated and tested under both quasi-static and dynamic (v = 7 m/s) conditions. Compared to the Miura-ori structure, the truncated origami showed higher specific energy absorption (SEA) and less load drop between the initial peak force and mean crushing force. In both loading directions, the SEA increased as the truncated ratio decreased for the truncated origami specimens, which was comparable under both quasi-static and dynamic loading. The truncated origami was extrapolated to a numerical model with 5 × 5 × 5 cells to mimic a block of material, and the effects of truncated ratio and loading velocity were investigated. As the e decreased, the deformation mode gradually changed from rigid folding and progressive deformation to plate buckling mode under quasi-static compression. This change was accompanied by an increase in both SEA and overall strength. The truncated origami exhibited the best energy absorption performance when e = 0.4. Under quasi-static compression in the x2- and x3-direction, the SEA of truncated origami is 3.2 and 1.6 times that of Miura-ori metamaterial, respectively. The truncated origami materials with a truncated ratio of 0.8 remained velocity-insensitive up to 25 m/s and displayed similar strength and deformation modes as under quasi-static loading. At a speed of 50 m/s the deformation became more localized, and the SEA increased significantly. The auxetic and expansion behaviors were significantly diminished under higher impact velocities.