The existing rock-fatigue-damage constitutive model fails to consider the influence of discharge energy and discharge times on the effect of rock damage under discharge impact. In this regard, the impact load test of sandstone was carried out. Based on the test results, the quantitative characterization formula of different discharge parameters on the weakening degree of rock compressive strength was established. Based on the TCK (Taylor−Chen−Kuszmaul) model, a constitutive model considering the mechanical properties of rock and the dynamic hange of micro-crack geometric size is established, and the cohesive model is proposed to calculate the crack size. The constitutive model includes the relationship between crack width, crack number, and rock compressive strength, and the change of damage factor D is used to consider the fatigue-damage effect of discharge shock on the rock. The results show that the modified model can quantitatively and accurately reflect the dynamic damage and failure process of rock and that the weakening of rock mechanical properties and the development of micro-cracks can be controlled by designing different discharge parameters.