Rocks present complex deformation behaviours and damage processes under triaxial cyclic loading—a subject not yet sufficiently researched. This paper performed triaxial multistage constant-amplitude cyclic loading experiments under different confining stresses on carbonaceous phyllite. The degradation process is analysed by investigating the variation of elastic modulusES, Poisson’s ratioυ, irreversible strainεirrand energy. Moreover, the rock’s failure mode is explored from both macro and micro perspectives. The results showed that the increase in stress level caused the decrease ofESin a step-like form, and the constant-amplitude cyclic loading in each stress level caused a slow decrease ofES, while theυincreased with stress level and constant-amplitude cycles in a similar form.εirraccumulated rapidly at first and then slowly at each stress level; the stress level and irreversible axial strain are related by an exponential function. In terms of energy evolution analysis, the damage to rock can be represented by the cumulative damage energy, there were deceleration accumulations and stability accumulation stages of damage at all stress levels, and an acceleration accumulation stage occurred when the rock was close to failure. The failures of rock under cyclic loading are mainly shear failures, accompanied by grain crushing.