Headcut erosion occurs in the development of a cohesive embankment breach and plays an important role in the breaching process. The headcut development is a mixed process of sediment erosion and mass failure. Based on momentum equilibrium, the critical incipient velocity is derived from the forces of particle weight under water, cohesive force among particles around the clay particle, uplift force, and drag force. Via the turbulent boundary layer flow theory, the critical stress can be connected with these forces. The formulae for the incipient stress and the critical velocity have been calibrated and validated with the results of undisturbed clay tests. A moment equilibrium-based method is proposed to simulate the headcut development and migration in a cohesive embankment breach due to overtopping flow. The hypothesis is given that the particle and mass is removed in the minimum moment on the breach slope. It is found that the tested results give good predictions of the headcut erosion development on the breach slope by validating laboratory data. The proposed method can be important and valuable to predict the breaching process in cohesive embankments.