Recently, significant attention has been directed towards two-dimensional Janus materials owing to their unique structure and novel properties. In this work, we have introduced novel two-dimensional Janus monolayers, SZrAZ₂ (A = Si, Ge; Z = P, As), through first principles. Our primary focus was the investigation of the controllable electronic properties exhibited by the Janus SZrAZ₂ structures under the influence of strain and an external electric field. Our research findings indicate the dynamic and thermodynamic stability of Janus SZrAZ₂ (A = Si, Ge; Z = P, As) monolayers. In the equilibrium state, these monolayers exhibit properties of an indirect band gap semiconductor. When subjected to biaxial strain and an external electric field, we observed that the dependency of SZrSiAs₂ and SZrGeAs₂ monolayers on an external electric field is very weak. Their electronic properties can only be modulated by applying biaxial strain. For SZrSiP₂ and SZrGeP₂ monolayers, their electronic properties can be modulated under biaxial strain and an external electric field, resulting in a transition from semiconducting to metallic behavior. Finally, we calculated the carrier mobility of these four structures and observed that the SZrGeAs₂ monolayer exhibits a hole mobility of up to 597.52 cm² s⁻¹ V⁻¹ in the x-direction, whereas the SZrSiP₂ monolayer demonstrates an electron mobility of up to 479.30 cm² s⁻¹ V⁻¹ in the y-direction. In the x-direction, the electron mobility of SZrSiAs₂ and SZrGeP₂ monolayers was measured to be 189.88 and 528.44 cm² s⁻¹ V⁻¹, respectively. These values are greater than or equivalent to that of experimentally synthesized MoS₂ (∼200 cm² s⁻¹ V⁻¹). Our research lays the foundation for utilizing two-dimensional Janus materials in electronic devices.