Rockmass may be in a creep state for a long time during underground mining. The failure progress of surrounding rock mass may be accelerated due to the mining disturbance. The rockmass failure is usually later than the mining activities and shows an obvious time lag effect, which brings difficulty in predicting the occurrence of engineering disaster. Given this problem, impact-creep tests of rock specimens were conducted under multi-cycle drop weight using a rock rheology-impact test machine. The changing law of axial strain of sandstone specimens was analyzed. The influence of creep state, impact times of drop weight, and impact energy on the deformation and failure characteristics of creep rock were discussed. In terms of energy point of view, the failure rule of creep rock was explained under impact disturbance. The test results show that under the same rock creep state, the internal rock damage increases gradually with the increase of impact energy and impact times. The formation process of the damage zone was accelerated and the energy utilization rate was increased, which leads to the accelerated creep failure of rock samples. The impact disturbance causes the accumulated elastic strain energy within rock specimen to be released directionally along the damage zone and damage occurs. The research results provide a theoretical basis for the prediction of delayed rockburst disasters.