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Abstract Searching for two-dimensional (2D) group V materials with ferromagnetism, elastic anisotropy, and carrier mobility and tunable band structure is one key to developing constantly developing nanodevices. The 2D monolayers SnxPy with x/y (1/1, 1/2, 1/3, and so on) coordination number are studied based on the particle-swarm optimization technique combined with the density functional theory optimization. Its thermal stability can be confirmed by molecular dynamics at 70K and 300K, indicating that the novel 2D materials have a stable existence. The electronic band structures of four stable structures suggest that all the monolayers of SnxPy are fully adjustable and flexible tunable band gaps semiconductors under the biaxial strain. The monolayer of P 4 ¯ 2 1 $$ \overline{4}{2}_1 $$ m-SnP2 with unique valence band structure can go from nonmagnetic to ferromagnetic by the hole doping because of the “Stoner criterion,” and Pmc21-SnP2 is a direct-like gap semiconductor with in-plane elastic anisotropy to possess a high electron mobility as high as 800 cm2V−1 s−1 along the k b direction, which is much higher than that of MoS2 (∼ 200 cm2V−1 s−1). The optical absorption peak of the material is in the ultraviolet region. These discoveries expand the potential applications of the emerging field of 2D SnxPy structures in nanoelectronics.