The mechanical behaviors of a series of two-dimensional (2-D) crystals X3M2 (X = S, Se; M = N, P, As) are explored through density functional theory (DFT) calculations. Two atomic structures exist for 2-D X3M2, namely α-heart and β-heart, which exhibit different out-of-plane Negative Poisson's Ratio (NPR) phenomena. For α-heart structures, a general out-of-plane NPR exists under in-plane tension in the y direction, while for β-heart type structures, a general NPR exists under in-plane tension in the x direction. Through DFT calculations, we revealed that a NPR is a general phenomenon for 2-D X3M2 with heart-shaped atomic structures, and the absolute value of the out-of-plane NPR for 2-D X3M2 is always one order of magnitude larger than other 2-D crystals reported before. At the same time, the in-plane NPR at certain angles around two in-plane principal axes also exists for 2-D X3M2 except for S3P2 due to the special heart-shaped structure. The coexistence of out-of-plane and in-plane NPRs for 2-D crystals has not been reported before and these special three-dimensional (3-D) auxetic properties in 2-D crystals may enormously enrich research studies on novel mechanical, electrical and chemical behaviors of 2-D crystals. This discovery will extend the family of 2-D crystals with a NPR and also provide new insights for designing novel negative Poisson's ratio materials. © 2019 the Owner Societies.