The horizontal stress in the fractured blocks of a fractured zone is in a stress relief status under repeated mining disturbances. To investigate the effect of the horizontal stress in fractured blocks on the stability of the overlying strata, uniaxially graded cyclic loading and unloading experiments on red sandstone with different initial stress level were carried out. First, the evolution of the loading and unloading elastic modulus, irreversible strain and load-unload response ratio were analyzed. Then, the strain energy evolution and damage variable characteristics were examined. Finally, the stability of a voussoir beam structure under repeated mining disturbances was discussed. The results showed that with increasing cycle number, the elastic modulus showed a nonlinear decreasing trend, the load-unload response ratio always fluctuated at approximately 1, and the irreversible strain showed a rapid and steady increasing trend. The proportion of elastic energy tended to increase linearly with increasing cycle number, while the proportion of dissipated strain energy tended to decrease. Moreover, the damage variable, based on the dissipation strain energy definition, showed a parabolic growth trend with increasing cycle number. The irreversible strain and damage variables showed an “increasing–decreasing-increasing” trend as the initial stress level increased. Finally, a stability criterion of the voussoir beam structure based on the effect of repeated mining disturbances on horizontal thrust was proposed. This research has important implications for overlying strata stability.