Graph Neural Networks have found widespread application in the field of precision medicine, particularly for predicting drug responses in cell lines, which imposes greater demands on the interpretability of prediction results. However, current graph interpretability algorithms tend to emphasize generality and overlook the complex interactions in drug data, making it difficult to attribute predictions to individual factors and limiting their use in predicting cancer drug responses. In this paper, we propose CETExplainer, a novel post-hoc interpretability algorithm built upon a multi-relational graph neural network-based framework for drug response prediction. We model drug response data using a multi-relational graph and enhance feature representations through both contrastive learning and multi-task learning. Furthermore, we introduce an interpretability mechanism based on a controllable edge-type-specific weighting scheme. It considers the mutual information between subgraphs and predictions, proposing a structural scoring approach to provide fine-grained, intuitive explanations for predictive models. We also introduce a method for constructing ground truth based on real-world datasets to quantitatively evaluate the proposed interpretability algorithm. The experimental results achieved a prediction AUC of 0.942 interpretability precision of 0.7134, outperforming the baseline methods. Qualitative experiments further demonstrated that our model can capture meaningful structures, providing a promising solution to the black-box challenge in drug response prediction.