Recently, ferroelectric materials have attracted considerable research attention. In particular, two dimensional (2D) ferroelectric materials have been considered as most crucial for next-generation circuit designs because of their application as novel electric memory devices. However, a 2D ferroelectric material is very rare. The ferroelectric materials with the form ABP2X6 (A = Ag, Cu; B = Bi, In; X = S, Se) are of interest because of their ferroelectric property maintained in their ultrathin structures. Within the ABP2X6 monolayer, the P―P bonds form the pillars that hold the top and bottom X planes, while the off-center A―B atoms between the X layers induce a spontaneous ferroelectric polarization. If the two off-center A―B sites are equally aligned, this would lead to the appearance of the paraelectric state. Such intriguing structures must impart novel mechanical properties to the materials. Until now, there has been no report on the mechanical properties of monolayer ABP2X6. Based on ﬁrst-principles calculations, we studied the structural, electronic, mechanical as well as the electromechanical coupling properties of monolayer ABP2X6 (A = Ag, Cu; B = Bi, In; X = S, Se). We found that they are all semiconductors with wide bandgaps of 2.73, 2.17, 3.00, and 2.31 eV for CuInP2Se6, CuBiP2Se6, AgBiP2S6, and AgBiP2Se6, respectively, which are calculated based on the Heyd-Scuseria-Ernzerhof (HSE) exchange correlation functional model. The conduction band minimum is mainly from p orbitals of X and B atoms, whereas the valence band maximum is due to the hybridization of the p orbital of X atoms and the d orbital of A atoms. Moreover, there are three short and three long A/B―X bonds due to the A―B off-center displacement. Together with the d-p orbital hybridization, the main reason for the distorted ferroelectric structure in ABP2X6 monolayers is the Jahn-Teller effect. ABP2X6 monolayers are predicted to be a new class of auxetic materials with an out-of-plane negative Poisson's ratio, i.e., the values of the negative Poisson's ratio are in the order AgBiP2S6 (−0.805) < AgBiP2Se6 (−0.778) < CuBiP2Se6 (−0.670) < CuInP2S6 (−0.060). This is mainly due to the tensile strain applied in the x/y direction enlarging the angle between P―P bonds and top layer X atoms, thereby enhancing the bucking height of monolayer ABP2X6. Moreover, external strain has a significant impact on the A―B off-center displacement, rendering an out-of-plane piezoelectric polarization. The values of e13 for CuInP2S6, CuBiP2Se6, AgBiP2S6
, AgBiP2Se6 monolayers are calculated to be −3.95 × 10−12, −5.68 × 10−12, −3.94 × 10−12, −2.71 × 10−12 C∙m−1, respectively, which are comparable to the only experimentally confirmed 2D out-of-plane piezoelectric Janus system (piezoelectric coefficient = −3.8 × 10−12 C∙m−1). This unusual auxetic behavior, ferroelectric polarization, and the electromechanical coupling in monolayer ABP2X6 could potentially lead to enormous technologically important applications in nanoelectronics, nanomechanics, and piezoelectrics.