Binary bilevel programs are challenging to solve due to the lack of compact single-level reformulations. Recent extended network flow-based reformulations have emerged as a promising approach, providing strong dual bounds. However, their increasing size can make them computationally prohibitive. We develop a cutting-plane framework that exploits these networks without requiring an extended-space formulation. We introduce two exact network flow-based reformulations and provide an efficient separation procedure for inequalities that certify the follower’s optimality. We further strengthen these inequalities through a tilting procedure that leverages the combinatorial structure of the networks. Computational experiments show that the proposed approach becomes increasingly advantageous as networks grow larger or more numerous. Moreover, incorporating the cuts into state-of-the-art bilevel solvers improves solution times and optimality gaps on BOBILib instances, closing eight more open instances than the baseline solvers. These results demonstrate the effectiveness of using network representations as separation oracles for binary bilevel optimization.