Interactions between individuals in cyber-physical systems can be described by complex networks. Complex network failures caused by attacking or corrupting on certain nodes would lead the network out of control. Cut vertexes are a kind of key nodes whose removal will disconnect a network. Cut vertexes play an important role in ensuring the connectivity of a network, however, it is still uncertain about the effect of cut vertexes-removal on network controllability. Therefore, we firstly investigate the model of network controllability based on cut vertexes-removal, and study the effect of cut vertexes-removal on controllability, meanwhile, random failures of nodes and target attacks based on degree are chosen as comparisons. The results demonstrate that random-failures have little effect on controllability, while cut vertexes-removal and target-attacks have a greater influence; when the average degree is low, the cut vertexes-removal and the target-attacks have nearly the same effect on controllability, but as the average degree grows, the cut vertexes-removal are more effective on controllability comparing with target-attacks; in addition, the controllable robustness of a network against cut vertexes-removal can be improved with the increase of average degree.