Cyber-physical power systems are susceptible to cyber threats and attacks that can lead to cascading failures and widespread power outages. Therefore, mitigating the impact of such attacks requires the timely implementation of operational strategies to prevent cascading blackouts. One Such strategy is the controlled islanding of the affected power grid, serving as a last resort against the propagation of the cascading outages. In this context, this paper introduces a novel detection-informed operational mitigation strategy, i.e., controlled islanding, against cyberattack-induced cascading failures, addressing 'when' and 'where' to implement controlled islanding. The proposed strategy leverages dynamic cascading failure modeling to quantify the impact of ongoing cyberattacks on power grids, using quantitative metrics such as demand-not-served (DNS). For effective operational mitigation, the strategy initiates controlled islanding when any attack, including fabricated protection trip commands and measurements' replay attacks, are detected, and any operating limits, such as line loading, are violated. It then proceeds to the implementation of controlled islanding, where identified cyberattack-affected elements are effectively surrounded by stable and self-sufficient islanded areas, while minimizing the system DNS. Numerical results on the IEEE 39-bus system demonstrate the effectiveness of the proposed strategy, reducing the DNS value by up to 47% when the controlled islanding strategy is implemented.