Two-dimensional (2D) materials with excellent properties are emerging as promising candidates in electronics and spintronics. In this work, a novel GaOCl monolayer is proposed and studied systematically based on first-principles calculations. With excellent thermal and dynamic stability at room temperature, its wide direct bandgap (4.46 eV) can be further modulated under applied strains. The 2D semiconductor exhibits high mechanical flexibility, and anisotropy in Poisson's ratio and carrier mobilities, endowing it with a broad spectrum of electronic and optoelectronic applications. More importantly, the GaOCl monolayer has spontaneous magnetization induced by hole doping and shows outstanding multidirectional piezoelectricity, which are comparable with those of either magnetic or piezoelectric 2D materials. Our calculations indicate that the GaOCl monolayer with wide bandgaps and tunable piezoelectricity and ferromagnetism could be promising for applications in multifunctional integrated nano-devices with high performance.