Graph similarity search aims to retrieve the subgraphs similar to a query graph from a graph database, which is a fundamental problem in graph database research and finds applications in various fields, e.g., bioinformatics and social networks. Graph edit distance (GED) between graphs is the core operation in graph similarity search. However, as GED computation is NP-hard, traditional filtering-verification frameworks face efficiency limitations in the filtering stage. In addition, static partitioning strategies used in existing methods cannot dynamically adapt to varying GED thresholds and still suffer from large-scale data sets. To address these issues, in this paper, we first propose a dynamic multi-layer graph partitioning strategy, which dynamically selects optimal partition layers to improve the filtering efficiency. Based on this, we design a compact index structure STree, which eliminates the need for extensive subgraph isomorphism verification, significantly improving query efficiency. Finally, we conduct comprehensive evaluations over two real datasets to demonstrate that our STree outperforms the state-of-the-art solution by up to one order of magnitude in terms of query time.