Tumor heterogeneity presents a significant challenge in predicting drug responses, especially as missense mutations within the same gene can lead to varied outcomes such as drug resistance, enhanced sensitivity, or therapeutic ineffectiveness. These complex relationships highlight the need for advanced analytical approaches in oncology. Due to their powerful ability to handle heterogeneous data, graph convolutional networks (GCNs) represent a promising approach for predicting drug responses. However, simple bipartite graphs cannot accurately capture the complex relationships involved in missense mutation and drug response. Furthermore, Deep learning models for drug response are often considered "black boxes", and their interpretability remains a widely discussed issue. To address these challenges, we propose an Interpretable Dynamic Directed Graph Convolutional Network (IDDGCN) framework, which incorporates four key features: (1) the use of directed graphs to differentiate between sensitivity and resistance relationships, (2) the dynamic updating of node weights based on node-specific interactions, (3) the exploration of associations between different mutations within the same gene and drug response, and (4) the enhancement of interpretability models through the integration of a weighted mechanism that accounts for the biological significance, alongside a ground truth construction method to evaluate prediction transparency. The experimental results demonstrate that IDDGCN outperforms existing state-of-the-art models, exhibiting excellent predictive power. Both qualitative and quantitative evaluations of its interpretability further highlight its ability to explain predictions, offering a fresh perspective for precision oncology and targeted drug development.