The experimentally verified negative Poisson's ratio of black phosphorus allows the extension of the medical and defense applications to the nanoscale regime without any artificial engineering. With a structure analogous to monolayer black phosphorus, monolayer SiS, SiSe, SnTe, and W-phase antimonene are predicted to show auxetic behavior, while a W-phase antimonene does not by using first-principles calculations. By putting these systems into a collective perspective with other puckered two-dimensional (2D) materials, we further formulate a uniform mechanism that could explain the different types of out-of-plane Poisson's ratio in the puckered 2D materials including monolayer group V-enes (BP, As, and Sb) and group IV monochalcogenides (SiS, SiSe, GeS, GeSe, SnS, SnSe, and SnTe). We found that both the structure and composition of the puckered monolayers play important roles in the out-of-plane Poisson's ratio.