We propose a conceptual design of optical power limiters with abrupt limiting action and enhanced power-handling capabilities that is based on exceptional point degeneracies (EPDs). The photonic circuit consists of two coupled cavities with differential Q factors. One of the cavities includes a Kerr-like nonlinear material. The underlying mechanism that triggers an abrupt transmittance suppression relies on the interplay between a nonlinear instability and an abrupt destruction of EPDs due to a resonance detuning occurring when the incident power exceeds a critical value. Our proposal opens up possibilities for the use of EPDs in optical power switching, Q switching, routing, and so on.