The Canadian supercritical water-cooled reactor concept features a re-entrant fuel channel wherein coolant first travels down a center flow tube and then up around the fuel elements. Previous work demonstrated that in cases of sudden coolant flow reduction or reversal (such as that which would result from a large pipe break near the core inlet), the coolant density reduction around the fuel has a positive reactivity effect that results in a power excursion. Such a transient is inherently self-terminating since the inevitable density reduction in the center flow tube has a very large negative reactivity effect. Nevertheless, a brief power pulse would ensue. In this work, the possibility of mitigating the power pulse with a fast-acting shutdown system was explored. The shutdown system model, consisting of bottom-inserted neutron absorbing blades and realistic estimates of insertion rates and trip conditions, was added to a full-core coupled spatial neutron kinetics and thermal-hydraulics model. It was demonstrated that such a system can effectively mitigate both the peak magnitude of the power excursion and its duration.