Given a large collection of tree-structured objects (e.g., XML documents), the similarity join finds the pairs of objects that are similar to each other, based on a similarity threshold and a tree edit distance measure. The state-of-the-art similarity join methods compare simpler approximations of the objects (e.g., strings), in order to prune pairs that cannot be part of the similarity join result based on distance bounds derived by the approximations. In this paper, we propose a novel similarity join approach, which is based on the dynamic decomposition of the tree objects into subgraphs, according to the similarity threshold. Our technique avoids computing the exact distance between two tree objects, if the objects do not share at least one common subgraph. In order to scale up the join, the computed subgraphs are managed in a two-layer index. Our experimental results on real and synthetic data collections show that our approach outperforms the state-of-the-art methods by up to an order of magnitude.