The fracture threshold of the woven carbonfiber/epoxy plates with singleside notch under combined mechanical loading and heating by incident beam is studied experimentally and theoretically. The threshold curve was measured and the fracture modes were identified through the observation of microscopy, they are thermal stressing, thermal thinning and thermal puncture. For the mode of thermal stressing corresponding to lower power laser beams, a theoretical criterion of the fracture is developed based on the analysis with fracture mechanics, in agreement with the experimental result.