Currently, research on the dynamic behavior features of coal and rock masses only considers the influence of original geological processes such as temperature and confining pressure, without considering the impact of cyclic stress generated during coal mining on the dynamic features of coal. And the determination of the dynamic features of coal is based on the index of coal bursting liability. The impact of cyclic stress damage on coal bursting liability and its dynamic features has not been thoroughly studied. In order to solve the above problems, cyclic stress damage tests are conducted on coal samples. The variation features of coal bursting liability under two cyclic stress damage conditions, namely constant upper and lower limits and variable upper limits, are analyzed. The experimental results show the following points. ① The static compressive strength of coal under the action of constant upper and lower limit cyclic stress and variable upper limit cyclic stress has decreased by 13.86% and 16.00%, respectively. Cyclic stress can degrade the mechanical strength of coal. ② The remaining elastic energy index of the original coal body is 27.34 kJ·m−3. It indicates that the coal body has a weak bursting liability. After constant upper and lower limit cyclic stress damage and variable upper limit cyclic stress damage, the remaining elastic energy index of the coal body has decreased by about 26.30% and 36.14%, respectively. It indicates that cyclic stress has a significant weakening effect on the bursting liability of the coal body. ③ As the remaining elastic energy index of the coal decreases, the dynamic compressive strength and dynamic elastic modulus of the coal decrease, while the dynamic failure deformation continuously increases. It indicates that the bursting liability of the coal will directly affect its dynamic features. The greater the bursting liability of the coal, the higher the degree of degradation of its impact dynamics related parameters. ④ As the remaining elastic energy index of the coal body continues to decrease, the fractal dimension of coal fragmentation after impact decreases. It indicates that cyclic stress leads to insufficient disintegration of the coal body after impact and weakened dynamic response.