In this study, we systematically investigated the structural, mechanical, electronic and optical properties of Sn2Bi monolayer, a sheet experimentally synthesized recently [PRL, 121, 126801 (2018)] which has been hydrogenated (Sn2BiH2) to stabilize free-standing form using density functional theory (DFT). For tuning the band structure and electronic properties, the mechanical strain and electric field are used. Our investigations show that in this free-standing sample, there are electron flat bands and free hole bands like the recently synthesized sample on silicon wafer, which provide the possibility of having strongly localized electrons and free holes with high mobility. Also, the band gap of Sn2BiH2 monolayer has experienced a growth of 80% compared with the experimental sample. The relevant results to strain suggest that the band gap can be properly manipulated by biaxial strain (-13% to +21%) within a range from 0.2 to 1.6 eV. It should be mentioned that the stability and flexibility of the corresponding monolayer under tensile and compressive strain are due to the strong σ bonds between atoms. We also realized the strain can cause indirect-direct transition in the band gap. Furthermore, our optical findings indicate that the Sn2BiH2 monolayer has almost metallic properties in a specific range of UV spectrum and it is transparent in the IR and visible spectrum of electromagnetic radiation. All these tunable properties and nontrivial features portend that Sn2BiH2 monolayer has great potentials in applications as nearinfrared detectors, thermoelectric devices, field-effect transistors, sensors, photocatalysis, energy harvesting, and optoelectronics.