A mathematical model of rock breaking under pulsed jet is established by introducing the Johnson-Holmquist-Concrete constitutive relation and the smoothed particle hydrodynamics method. Based on this model, the formation, propagation and attenuation of stress wave during rock breaking by pulsed jet are simulated. The relations between pressure and time at different points on rock surface and the curve of peak stress wave versus distance to action spot are obtained. Destruction behaviors of rock under pulsed jet and effects on stress wave effect from jet velocity and lithology are studied according to the above calculation results, analysis results show that stress wave effect of pulsed jet acts locally and the peak stress wave shrinks sharply as the acting distance increases. The rock breaking mechanism of stress wave is tensile failure during the high speed process of load-unload. Power and effect range of stress wave is in high direct proportion with jet velocity. There is a threshold velocity before the macroscopic failure. Rocks of different lithologies have different destruction types under pulsed stress wave of pulsed jet. Destruction type of low strength rock like sandstone is crack propagation under the tensile stress during the high speed process of load-unload, while the destruction type of high strength brittle rocks like granite and limestone is vertical failure of stress concentration.