The design of two-dimensional (2D) auxetic semiconductors satisfying the rigorous requirements of photocatalytic water-splitting remains challenging. Anisotropic Janus monolayers display excellent potential for water splitting owing to their high photocatalytic activity, while their scarcity proves to be a disadvantage for wide application. Herein, we propose an anisotropic auxetic Janus 2D photocatalyst, a structurally stable ε-SnO monolayer, using first-principles calculations. Monolayer ε-SnO exhibits extraordinary flexibility due to its ultralow Young's moduli and high critical crack strain. Particularly, the large negative in-plane Poisson's ratios are predicted to be −0.14/-0.17 along the x-/y-direction, which are larger than most previously reported 2D materials. It has a wide indirect bandgap, straddling the redox potentials of water, which varies with the in-plane strain. Radiation-induced carriers can drive the simultaneous occurrence of both hydrogen (HER) and oxygen (OER) evolution half reactions, even when they are under strain. The anisotropic carrier mobility can reach 625.86 cm2·V−1·s−1 and the absorption coefficients are predicted to reach up to the order of 105 cm−1, which is favorable for the photoexcited carrier to migrate to the active sites for water splitting. Interestingly, after transition metal atoms (from Sc to Zn) decoration, Mn/ε-SnO and Cr/ε-SnO as high-efficient single-atom HER photocatalysts are capable of driving HER with ultralow overpotentials of −0.002 V and −0.033 V, respectively, outperforming commercial Pt (−0.09 V). Meanwhile, the Cu/ε-SnO with a low-overpotential (0.385 V) is significantly better for neutral OER than IrO2 (0.55 V) that is widely accepted in industrial applications.