Two-dimensional (2D) materials with negative Poisson's ratio (NPR) attract considerable attention because of their exotic mechanical properties. We propose a new 2D material, monolayer GaPS4, which shows NPR for both in-plane (-0.033) and out-of-plane (-0.62) directions. Such coexistence of NPR in two distinct directions could be explained by its corner- and edge-shared tetrahedra pucker structure. GaPS4 has an ultralow cleavage energy of 0.23 J m-2 according to our calculation, such that exfoliation of the bulk material is feasible for the preparation of mono- and few-layer GaPS4. Direct wide band gap of 3.55 eV and moderate electron mobility have been revealed in monolayer GaPS4, while the direct gap feature is robust within a strain range of -6% to 6%. These findings render 2D GaPS4 a promising candidate for applications in nanoelectronics and low-dimensional electromechanical devices.