In the realm of biomedicine, the prediction of associations between drugs and diseases holds significant importance. Yet, conventional wet lab experiments often fall short of meeting the stringent demands for prediction accuracy and efficiency. Many prior studies have predominantly focused on drug and disease similarities to predict drug-disease associations, but overlooking the crucial interactions between drugs and diseases that are essential for enhancing prediction accuracy. Hence, in this paper, a resilient and effective model named Hierarchical and Dynamic Graph Attention Network (HDGAT) has been proposed to predict drug-disease associations. Firstly, it establishes a heterogeneous graph by leveraging the interplay of drug and disease similarities and associations. Subsequently, it harnesses the capabilities of graph convolutional networks and bidirectional long short-term memory networks (Bi-LSTM) to aggregate node-level information within the heterogeneous graph comprehensively. Furthermore, it incorporates a hierarchical attention mechanism between convolutional layers and a dynamic attention mechanism between nodes to learn embeddings for drugs and diseases. The hierarchical attention mechanism assigns varying weights to embeddings learned from different convolutional layers, and the dynamic attention mechanism efficiently prioritizes inter-node information by allocating each node with varying rankings of attention coefficients for neighbour nodes. Moreover, it employs residual connections to alleviate the over-smoothing issue in graph convolution operations. The latent drug-disease associations are quantified through the fusion of these embeddings ultimately. By conducting 5-fold cross-validation, HDGAT's performance surpasses the performance of existing state-of-the-art models across various evaluation metrics, which substantiates the exceptional efficacy of HDGAT in predicting drug-disease associations.