Power grid vulnerability analysis is often performed through solving a bi-level optimization problem, which, if solved to optimality, yields the most destructive interdiction plan with the worst loss. As one of the most effective operations to mitigate deliberate outages or attacks, transmission line switching recently has been included and modeled by a binary variable in the lower level decision model. Because this bi-level problem is a challenging nonconvex discrete optimization problem, no exact algorithm has been developed, and only a few recent heuristic procedures are available. In this paper, we present a novel trilevel reformulation of this bi-level problem, as well as its single level equivalent form, and describe a finitely-convergent cutting plane algorithm to derive an exact solution. Numerical results are provided and benchmarked against existing ones, which confirms the quality of solutions and the computational efficiency of our algorithm.