The next-generation spintronic device demands the gated control of spin transport across the semiconducting channel through the replacement of the external gate voltage source by the piezo potential, as experimentally demonstrated in Zhu et al. ACS Nano, 2018, 12 (2), 1811-1820. Consequently, a high level of out-of-plane piezoelectricity together with a large Rashba spin splitting is sought after in semiconducting channel materials. Inspired by this experiment, a new hexagonal buckled two-dimensional (2D) semiconductor, ZnTe, and its iso-electronic partner, CdTe, are proposed herewith. These 2D materials show a strong spin-orbit coupling (SOC), which is evidenced by a large Rashba constant of 1.06 and 1.27 eV·Å, respectively, in ZnTe and CdTe monolayers. Moreover, these Rashba semiconductors exhibit a giant out-of-plane piezoelectric coefficient (d33) = 88.68 and 172.61 pm/V, and can thereby generate a high piezo potential for gating purposes in spin field-effect transistors (spin-FETs). While the low elastic stiffness implies the mechanical flexibility or stretchability in these monolayers. The Rashba constants are found to be effectively modulated via external perturbations, such as strain and electric field. The wide band gap provides ample room for modulation in its electronic properties via external perturbations. Such scope is severely limited in previously reported narrow band gap Rashba semiconductors. The fascinating results found in this work indicate their great potential for applications in next-generation self-powered flexible-piezo-spintronic devices. Moreover, a new class of hexagonal buckled ZnX (X: S, Se, or Te) monolayers is proposed herein based on their previously synthesized bulk counterparts, while their electronic, mechanical, piezoelectric, and thermal properties have been thoroughly investigated using the state-of-art density functional theory (DFT).