Since the successful experimental synthesis of MoSi₂N₄, the “MA₂Z₄ family” has attracted the interest of researchers from many fields due to its excellent physical and chemical properties. In this work, we propose a novel two-dimensional Janus STiXY₂ (X = Si, Ge; Y = N, P, As) monolayer using first principles. Under biaxial strain and an applied electric field, we investigate the controllable electronic properties of Janus STiXY₂ (X = Si, Ge; Y = N, P, As) structures. Our predictions demonstrate that the 2D STiXY₂ materials are structurally and dynamically stable. Using the HSE functional, we show that these 2D STiXY₂ materials are indirect semiconductors with band gaps of 0.99, 1.142, 0.834, 1.322, 0.735, and 0.215 eV, respectively. Additionally, we found that, except for the STiXAs₂ (X = Si, Ge) monolayer, the influence of biaxial strain on electronic characteristics is significantly greater than that of the applied electric field. Finally, we calculated the carrier mobilities of these Janus structures and found that the STiGeP₂ monolayer has the highest electron carrier mobility in the x-direction with 8175.66 cm² s⁻¹ V⁻¹, while the STiGeAs₂ monolayer has the highest electron carrier mobility in the y-direction, 2897.94 cm² s⁻¹ V⁻¹. They are all larger than those of the experimentally synthesized MoS₂ (∼200 cm² s⁻¹ V⁻¹). The results may provide insights for the study of novel Janus monolayers with potential application in electronic devices.