Time series anomaly detection has garnered considerable attention across diverse domains. While existing methods often fail to capture the underlying mechanisms behind anomaly generation in time series data. In addition, time series anomaly detection often faces several data-related inherent challenges, i.e., label scarcity, data imbalance, and complex multi-periodicity. In this paper, we leverage causal tools and introduce a new causality-based framework, CaPulse, which tunes in to the underlying causal pulse of time series data to effectively detect anomalies. Concretely, we begin by building a structural causal model to decipher the generation processes behind anomalies. To tackle the challenges posed by the data, we propose Periodical Normalizing Flows with a novel mask mechanism and carefully designed periodical learners, creating a periodicity-aware, density-based anomaly detection approach. Extensive experiments on seven real-world datasets demonstrate that CaPulse consistently outperforms existing methods, achieving AUROC improvements of 3% to 17%, with enhanced interpretability.