Ending poverty in all its forms is the first of the 17 sustainable development goals (SDGs) of the 2030 Agenda for Sustainable Development. Therefore, it is of great significance to study poverty in the context of sustainable development. At present, the effect of income growth on poverty reduction is becoming less evident, whereas the effect of inhabitant heterogeneity on poverty reduction is becoming increasingly significant in China. Based on the original two-dimensional poverty decomposition of income growth and redistribution, this study introduces the heterogeneity effect to decompose rural poverty in China from three dimensions. It first decomposes the change in income distribution into mean, variance, and residual effects using counterfactual analysis. Then, it introduces the Foster–Greer–Thorbecke index decomposition to decompose China’s rural poverty under the different poverty line. In addition, this paper employs mathematical statistics to analyze the effects of poverty’s growth, dispersion, and heterogeneity. This study finds that the three-dimensional poverty decomposition method can measure the trajectory and trend of poverty more precisely and comprehensively. Moreover, it found that the contradiction between economic growth and poverty regression is due to the fact that the poverty reduction effect of the growth effect and the poverty alleviation effect of the discrete effect have asymmetrical characteristics, whereas the discrete effect and the heterogeneous effect have symmetrical characteristics; that is, the poverty reduction effect of income growth is insufficient to compensate for the poverty deepening effect brought about by the widening income gap, and that the heterogeneous poverty reduction effect plays an increasingly important role. Therefore, to prevent residents from falling back into poverty after being lifted out of it, we must reduce the widening income gap. Moreover, residents’ ability to reduce poverty on their own must be strengthened.