Multivariate time series anomaly detection has numerous real-world applications and is being extensively studied. Modeling pairwise correlations between variables is crucial. To explicitly capture spatial dependencies between variables, existing methods use learnable graph structures and graph neural networks. However, these methods are primarily trained based on prediction or reconstruction, which can only learn similarity relationships between sequence embeddings and cannot explain the role of graph structure in the evolution of time series. In this paper, we designed a framework that models spatial dependencies using interpretable causal relationships and detects anomalies through changes in causal patterns. Specifically, we propose a method to dynamically discover Granger causality effects using gradients in nonlinear deep predictors and employ a simple sparsification strategy to obtain a Granger causality graph, detecting anomalies from a causal perspective. Experiments on real-world datasets demonstrate that the proposed model detects anomalies more accurately than baseline methods.