Recently, Graph Neural Networks (GNNs) have gained widespread application in automatic brain network classification tasks, owing to their ability to directly capture crucial information in non-Euclidean structures. However, two primary challenges persist in this domain. First, within the realm of clinical neuro-medicine, signals from cerebral regions are inevitably contaminated with noise stemming from physiological or external factors. The construction of brain networks heavily relies on set thresholds and feature information within brain regions, making it susceptible to the incorporation of such noises into the brain topology. Additionally, the static nature of the artificially constructed brain network's adjacent structure restricts real-time changes in brain topology. Second, mainstream GNN-based approaches tend to focus solely on capturing information interactions of nearest neighbor nodes, overlooking high-order topology features. In response to these challenges, we propose an adaptive unsupervised Spatial-Temporal Dynamic Hypergraph Information Bottleneck (ST-DHIB) framework for dynamically optimizing brain networks. Specifically, adopting an information theory perspective, Graph Information Bottleneck (GIB) is employed for purifying graph structure, and dynamically updating the processed input brain signals. From a graph theory standpoint, we utilize the designed Hypergraph Neural Network (HGNN) and Bi-LSTM to capture higher-order spatial-temporal context associations among brain channels. Comprehensive patient-specific and cross-patient experiments have been conducted on two available datasets. The results demonstrate the advancement and generalization of the proposed framework.