Supervalid inequalities are a specific type of constraints often used within the branch-and-cut framework to strengthen the linear relaxation of mixed-integer programs. These inequalities share the particular characteristic of potentially removing feasible integer solutions as long as they are already dominated by an incumbent solution. This paper focuses on supervalid inequalities for solving binary interdiction games. Specifically, we provide a general characterization of inequalities that are derived from bipartitions of the leader's strategy set and develop an algorithmic approach to use them. This includes the design of two verification subroutines that we apply for separation purposes. We provide three general examples in which we apply our results to solve binary interdiction games targeting shortest paths, spanning trees, and vertex covers. Finally, we explore a connection between the proposed supervalid inequalities and a specific type of set system called greedoids.