This work systematically studies the mechanical responses of a novel semiconducting Janus MoSSe monolayer subjected to uniaxial tensile loadings by molecular dynamics simulations. It is found that the Janus MoSSe monolayer shows clearly anisotropic responses along armchair direction and the zigzag direction. The phase transition behavior is observed when the Janus MoSSe monolayer is under the action of tension along the 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 with temperature increasing. Particularly, the ductile-to-brittle fracture behavior is observed when uniaxial tension is applied along the zigzag direction depending on temperatures. The underline fracture mechanism is analyzed. Moreover, mechanical properties of Janus MoSSe monolayer with various grain boundaries are also carefully explored. It is found that the ultimate strength and ultimate strain depend more sensitively on narrow grains than on those wider ones. The crack is initialized near the grain boundaries and propagates along the direction almost perpendicular to the grain boundaries. The findings of this work may shed light on design and optimization of nanoscale electronic devices based on the Janus MoSSe monolayers.