Recently, two-dimensional (2D) metal sulfide halides have attracted much attention due to their unique magnetic and electronic properties. In this work, we design a family of 2D MSXs (M = Ti, V, Mn, Fe, Co, and Ni, X = Br and I) and investigate their structural, mechanical, magnetic, and electronic properties based on first-principles calculations. We find that TiSI, VSBr, VSI, CoSI, NiSBr, and NiSI are kinetically, thermodynamically, and mechanically stable. Other 2D MSXs are unstable because MnSBr, MnSI, FeSBr, FeSI and CoSBr show significant imaginary phonon dispersions and TiSBr has a negative elastic constant (C44). All stable MSXs are magnetic, and their ground states vary with different compositions. TiSI, VSBr, and VSI are semiconductors with anti-ferromagnetic (AFM) ground states, while CoSI, NiSBr, and NiSI are half-metallic and ferromagnetic (FM). The AFM character is contributed by the super-exchange interactions, while the FM states are related to the carrier-mediated double-exchange. Our findings demonstrate the effectiveness of composition engineering in designing novel 2D multifunctional materials with properties suitable for various applications.