Two-dimensional (2D) Janus materials exhibit an outstanding potential that can meet the rigorous requirements of photocatalytic water splitting resulting from their unique atomic arrangement. However, these materials are quite scarce. Through ab initio density functional theory calculations, we introduce a kagome topology into the honeycomb lattice of blue phosphorene using phosphorus and bismuth atoms to build a hybrid honeycomb-like kagome lattice, realized by a hitherto unknown kagome-like Janus-like BiP3 monolayer with robust stability. Excitingly, the out-of-plane asymmetry benefiting from kagome and honeycomb topologies gives rise to a significantly negative out-of-plane Poisson's ratio and an obvious built-in electric field pointing from the sublayer of the P atom to the sublayer of the Bi atom. In conjunction with the investigations that encompass semiconducting properties, such as a quasi-direct gap, suitable band-edge positions, effective visible-light absorption, and high carrier mobility, the BiP3 monolayer achieves overall water splitting at pH 0-14 regardless of strain. Moreover, this intrinsic electric field provides a sufficient photogenerated carrier driving force for water splitting. The bare BiP3 comprises P and Bi atoms that function as catalysts for the hydrogen evolution reaction (HER) and oxygen evolution reaction (OER) active sites, respectively. Upon exposure to light, the reaction of water into H2 and O2 can be observed across a pH range of 0-14. Meanwhile, by designing a transition-metal single-atom catalyst (TM@BiP3), our investigations have shown that embedding a single TM on BiP3 is a feasible route to improving the HER/OER activity by reducing the overpotentials to -0.039 and 0.58 eV for Mo and Os atoms, respectively. In this case, the positive value of the external potential acts as a sufficient OER driving force, i.e., in the light environment, the Os@BiP3 system can promote water molecules spontaneously oxidized into O2 at pH 0-14.