The dynamic compression responses of quartz sands of different grain sizes and gradations are tested with a modified spilt Hopkinson pressure bar in which a single-pulse loading system is implemented. The yield stresses, the compressibility and the energy-absorption densities of the granular materials are calculated from the compression curves. The effects of the grain size and the gradation on those dynamic macro responses are investigated and presented. The grain size distributions of the samples after loading are obtained with a laser diffractometry instrument, and are analyzed quantitatively with the Hardin relative breakage index. The effects of the grain-scale properties on the dynamic macro responses of granular materials can be interpreted well with the particle breakage mechanism. The Theoretical analyses show that the energy-absorption density and the particle breakage extent are linearly related to the logarithm of axial stress respectively, and the slopes are both proportional to the compressibility. Moreover, a simple model for predicting the dynamic energy-breakage efficiency of the granular materials is derived. Based on the discrete element method (DEM), simulation of the granular material under one-dimensional dynamic compression is conducted to further interpret the experimental results. The size dependence of the coordination number of grains and its influence on particle breakage is discussed.