A series of numerical experiments is performed to investigate the breaking of obliquely incident internal waves propagating towards a bottom slope. The case of critical reflection is considered, where the angle between the wave group velocity vector and the horizontal matches the bottom slope angle. The flow evolution is found to be significantly different from the evolution observed previously in simulations of normally incident waves. The divergence of the Reynolds stress in the breaking zone causes a strong along-slope mean current, which changes the flow structure dramatically. The wave does not penetrate the current but breaks down at its upper surface as the result of a critical layer interaction. A continuously broadening mean along-slope current with an approximately constant velocity is produced. We propose a simple model of the process based on the momentum conservation law and the radiation stress concept. The model predictions are verified against the numerical results and are used to evaluate the possible strength of along-slope currents generated by this process in the ocean.