Constructing Z-scheme heterojunction photocatalysts with high solar-to-hydrogen (STH) efficiency is a practical alternative to produce clean and recyclable hydrogen energy on a large scale. This paper presents the design of stable Z-scheme blue phosphorene (BlueP)/γ-SnS heterostructures with excellent photocatalytic activities by applying strains. The first-principles calculations show that the BlueP/γ-SnS heterobilayer is a type-I heterojunction with an indirect bandgap of 1.41 eV and strong visible-light absorption up to 105 cm-1. Interestingly, biaxial strains (ε) can effectively regulate its bandgap width (semiconductor-metal) and induce the band alignment transition (type-I-type-II). Compressive and tensile strains can significantly enhance the interfacial interaction and visible-light absorption, respectively. More intriguingly, compressive strains can not only modulate the heterojunction types but also make the band edges meet the requirements for overall water splitting. In particular, the Z-scheme (type-I) BlueP/γ-SnS bilayer at -8% (-2%) strain exhibits a relatively high STH efficiency of 18% (17%), and the strained Z-scheme system (-8% ≤ ε ≤ -6%) also exhibits high and anisotropic carrier mobilities (158-2327 cm2 V-1 s-1). These strain-induced outstanding properties make BlueP/γ-SnS heterostructures promising candidates for constructing economically feasible photocatalysts and flexible nanodevices.