This work systematically studied mechanical responses of a novel semiconducting Janus MoSSe monolayer subjected to uniaxial tensile loadings by means of molecular dynamics simulations. It is found that the Janus MoSSe monolayer shows clearly anisotropic responses along armchair and zigzag directions. The phase transition behavior was observed when the Janus MoSSe monolayer is under tension along zigzag direction at temperatures below 100 K, while it does not exist in any other conditions. The Young’s modulus, ultimate strength and ultimate strain decrease as temperature increasing. Particularly, the ductile-to-brittle fracture behavior was observed when uniaxial tension is applied along zigzag direction depending on temperatures. The underline fracture mechanism was analyzed. Moreover, mechanical properties of Janus MoSSe monolayer with various grain boundaries were also carefully explored. It is found that the ultimate strength and ultimate strain depend more sensitively for narrow grains than those wider ones. The crack is initialized near the grain boundaries and propagated along direction almost perpendicular to the grain boundaries. The findings of this work may shed some lights on design and optimization of nanoscale electronic devices based on the Janus MoSSe monolayers.