Periodical cyclic loads are often encountered in the construction and operation stages of geotechnical engineering. In the paper, multi-level triaxial cyclic loading and unloading (TCLU) compression tests are conducted on sandstone samples under varying upper limits of axial stress. Firstly, the crack volumetric (deviatoric) strain curves and the characteristic stresses are obtained, and the evolution curves of the hysteresis loop, the characteristic of crack strain, and axial (radial) strain are analyzed. Secondly, the strain evolution equation has been applied to the fitting analysis of 125 groups of axial and radial strain data, and good results were obtained. The equation has better applicability to TCLU tests. Finally, the damage evolution law, life prediction of the sandstone, and failure mechanism are revealed. Studies show that: after the crack initiation stress is exceeded, the crack radial strain and the crack axial strain curves gradually show an obvious nonlinear phenomenon with the increase of axial stress. By fitting the evolution process of the axial (radial) strain, it clarified the coupling action of axial stress and confining pressure on the fatigue failure of sandstone. The damage factor of each sample shows a step growth, and the development of the radial damage factor lags behind the axial damage factor. Upper limits of axial stress value are key factors in determining the fatigue life of rocks. The rock failure mode under the TCLU path is mainly manifested as splitting tension failure and shear failure. The fatigue life is predicted by fitting and analyzing the rock strain evolution equation under the action of TCLU using damage mechanics theory combined with experimental data, which will help to understand the failure mechanism of rock mass, and then scientifically evaluate the long-term stability of engineering rock mass.