The detection of cut vertex is an important operation on graph. The deep-first search algorithm can solve this problem. However, the algorithm has drawback which prevents it from applying in the real-world applications. This is because of the two characteristics for today's data. One is the scale of data is huge, so it is challenging for many operations on graph. Another challenge is that the data is changeable. Because of the massive updates, the traditional algorithm must compute repeatedly according to the change, wasting a lot of time and space. The time complexity of deep first search tree is O(|V|+|E|), where |V| and |E| are number of nodes and edges of graph, so it can adapt to the first characteristic very well. But it is useless for the second characteristic. In order to solve this problem, this paper puts forward an algorithm based on compression to discovering cut vertex. The algorithm compresses the graph based on the naïve similarity on nodes. The time complexity of the algorithm is O(|E|). It discovers cut vertex on the lossless compression graph. At the same time, the algorithm maintains the updates of the nodes and edges dynamically, and updates the graph without decompression. It discovers cut vertex on the compression graph after update. These methods reduce the consumption of time and space remarkably. The compressed graph obtained by the compression algorithm in the article can be applied to other graph operations.