Despite a great progress has been made in 3D point cloud recognition, recent studies find that deep models are vulnerable to adversarial attacks generated through various point cloud transformations. However, existing spoofing attack methods neglect the influence of point cloud topology on the model recognition accuracy. In this paper, we propose a novel adversarial point cloud generation network, named Topology Destruction Network (TD-Net), which destroys topological structure of a point cloud by selectively dropping points leading to the formulation of holes on the surface. The network consists of an encoder and a decoder. The encoder first leverages a PointNet architecture to extract geometric information of the original point cloud, from which a topological adjacency matrix is encoded describing adjacency relationships between points. The decoder selects a specific point to drop associated with its neighboring points derived from the learned adjacency matrix, resulting in an adversarial point cloud with a destructed topology. Experiments on the ModelNet40 dataset demonstrate that the proposed method surpasses existing adversarial attacks in terms of reducing model recognition accuracy.