Although the α-SnWO4 material has recently been considered as a new good candidate for visible-light-driven photo(electro)chemical water splitting, the performance is still low and requires further improvement. Here, we present a deep fundamental work on the influence of the various possible facets exposed on this material for oxygen and hydrogen evolution reactions using hybrid density functional theory. The energetic, electronic, water redox, and charge carrier transport features of the four possible (100), (010), (001), and (110) facets (low-Miller index surfaces) are investigated, and significant anisotropic nature is revealed. The relevant properties of each facet to the water oxidation/reduction reactions are correlated with the surface W coordination number. Taking into account the stability and combining optoelectronic and water redox features together of each surface, our work demonstrates that the (110) facet is photocatalytically the best candidate for the OER, while the (100) facet is the best candidate for the HER. Their transport characteristics are found to be much better than those obtained for the three major (121), (210), and (111) facets of synthesized α-SnWO4 samples. Substitutional Ge at the Sn site and Mo at the W site on the two (110) and (100) facets are expected to increase the rates of the water oxidation/reduction reactions. An analysis of the reaction mechanism for the OER in (110)-oriented α-SnWO4 reveals a promising performance of this facet for electrocatalytic water oxidation. These outcomes will greatly motivate experimentalists for carefully designing (110)- and (100)-oriented α-SnWO4 samples to enhance the photo(electro)catalytic OER and photocatalytic HER performances.