Two-dimensional materials with high carrier mobility and tunable magnetism are in high demand for nanoelectronic and spintronic applications. Herein, we predict a novel two-dimensional monolayer KTlO that possesses an indirect band gap of 2.25 eV (based on HSE06 calculations) and high carrier mobility (450 cm2 V-1 s-1 for electrons and 160 cm2 V-1 s-1 for holes) by means of ab initio calculations. The electron mobility can be increased up to 26 280 cm2 V-1 s-1 and 54 150 cm2 V-1 s-1 for bilayer and trilayer KTlO, respectively. The KTlO monolayer has a calculated cleavage energy of 0.56 J m-2, which suggests exfoliation of the bulk material as a viable means for the preparation of mono- and few-layer materials. Remarkably, the KTlO monolayer demonstrates tunable magnetism and half-metallicity with hole doping, which are attributed to the novel Mexican-hat-like bands and van Hove singularities in its electronic structure. Furthermore, monolayer KTlO exhibits moderate optical absorption over the visible light and ultraviolet regions. The band gap value and band characteristics of monolayer KTlO can be substantially manipulated by biaxial and uniaxial strains to meet the requirement of various applications. All these novel properties make monolayer KTlO a promising functional material for future nanoelectronic and spintronic applications.