This paper proposed structural analysis and mathematical methods for destabilizing terrorist networks. The three different approaches are discussed for example: (i) cohesion analysis (such as cliques, ncliques, n-clans and k-plex) to determine familiarity, robustness and reachability within subgroups in 9/11 terrorist network; (ii) role analysis (such as position role index) to determine critical nodes (gatekeepers or leaders) and their removal leads to the maximum disruption of the network; (iii) power analysis (such as degree centrality, Eigenvector centrality and dependence centrality) to uncover the hidden hierarchy of terrorist networks. The methods are implemented in the software prototype known as iMiner, which may provides assistance to law enforcement agencies, indicating when the capture of a specific terrorist will likely disrupt the terrorist network.