Terrorist organizations have social networks that enable them to recruit and operate around the world. This paper presents a novel computational framework for derivation of optimal destabilization strategies against dynamic social networks of terrorists. We develop a game-theoretic model to capture the distributed and complex dynamics of terrorist organizations, and introduce a technique for estimation of such dynamics from incomplete snapshots of target networks. Furthermore, we propose a mechanism for devising the optimal sequence of actions that drive the internal dynamics of targeted organizations towards an arbitrary state of instability. The performance of this framework is evaluated on a model of the Al-Qaeda network in 2001, verifying the efficacy of our proposals for counter-terrorism applications.