Aiming at reducing the dynamic disasters such as rock fall and rock burst caused by deep strong disturbance, high damping rubber material with good anti-scouring and energy absorbing characteristics was applied to a new type of small strain energy absorbing bolt. To systematically evaluate the influence of geometric dimensions on the buffering and energy absorption properties of high damping rubber materials, the drop hammer impact system and SHPB device were used to carry out impact tests on high damping rubber samples and “rubber-granite” composite samples with different thickness-diameter ratios. Results of drop hammer impact system test show that under the same impact condition, the dynamic response of the material decreased with the increase of the thickness-diameter ratio and it tended to be stable when the thickness-diameter ratio was greater than 0.6. In addition, the peak value of each dynamic response of the material was less than 15% compared with the first dynamic response in six repeated impacts with the same drop distance. SHPB impact test results show that the maximum energy absorption rate was 0.336 at the thickness-diameter ratio of 0.3. Under the same pressure impact, the fractal dimension (D) of granite decreased with the increase of thickness-diameter ratio. When the thickness-diameter ratio was greater than 0.3, the D value tended to change steadily with smaller amplitude.