Anomaly detection is a crucial aspect of ensuring the on-orbit reliability of spacecraft. By identifying anomalies in telemetry data, the accuracy and reliability of spacecraft operations can be significantly improved. This paper considers both detection accuracy and timeliness to design a method for predicting the behavior of telemetry data based on Granger causality and support vector regression (SVR) models, combined with a clustering approach to achieve adaptive anomaly detection. First, Granger causality modeling is used to explore the causal relationships in the telemetry data. Based on the resulting causality graph, the SVR model is trained using data processed by principal component analysis (PCA) to obtain the prediction errors compared to the original data. Next, a preliminary threshold is determined using the mean squared error (MSE) to filter samples that may contain anomalies. Finally, clustering methods are applied to the errors to calculate the center and standard deviation of each cluster. Based on the clustering results, statistical measures such as skewness, kurtosis, and quantiles are adaptively used to select the anomaly threshold, further optimizing the anomaly detection performance. Experimental results indicate that the proposed method outperforms preset threshold and expert system-based methods in terms of accuracy and adaptability, reducing the false alarm rate by 78.7% and the miss alarm rate by 69.1%. This study’s method is applicable to various data types and scenarios, providing an effective reference for anomaly detection.