While graph representation learning methods have shown success in various graph mining tasks, what knowledge is exploited for predictions is less discussed. This paper proposes a novel Adaptive Subgraph Neural Network named AdaSNN to find critical structures in graph data, i.e., subgraphs that are dominant to the prediction results. To detect critical subgraphs of arbitrary size and shape in the absence of explicit subgraph-level annotations, AdaSNN designs a Reinforced Subgraph Detection Module to search subgraphs adaptively without heuristic assumptions or predefined rules. To encourage the subgraph to be predictive at the global scale, we design a Bi-Level Mutual Information Enhancement Mechanism including both global-aware and label-aware mutual information maximization to further enhance the subgraph representations in the perspective of information theory. By mining critical subgraphs that reflect the intrinsic property of a graph, AdaSNN can provide sufficient interpretability to the learned results. Comprehensive experimental results on seven typical graph datasets demonstrate that AdaSNN has a significant and consistent performance improvement and provides insightful results.