With the increase in mining depth, the deep hard rock mass is under threat of rockburst under high geostress, high temperature, high osmotic pressure, and strong disturbance. To reduce the probability and strength of rockburst, a new energy-absorbing bolt for guaranteeing the stability of deep hard rock mass was developed utilizing the energy absorption characteristic of high-damping rubber. To analyze the practicability and obtain the quantified behaviors of this new energy-absorbing bolt, a series of impact tests on specimens of high-damping rubber, granite, and granite–rubber composite specimens was carried out by a split Hopkinson pressure bar (SHPB) method. Further, considering the different working depths with different rock temperatures, the dynamic energy-absorbing characteristics of high-damping rubber under different temperatures were tested. The testing results show that the new energy-absorbing bolt can consume the storage energy in host rock effectively, and the environmental temperature will produce certain effects on the energy-consuming rate. In addition, the optimal energy-absorbing thickness–diameter ratio of high-damping rubber was confirmed by SHPB tests.