Anomaly detection in multivariate time series data is challenging due to complex temporal and feature correlations and heterogeneity. This paper proposes a novel unsupervised multi-scale stacked spatial-temporal graph attention network for multivariate time series anomaly detection (STGATMAD). The core of our framework is to coherently capture the feature and temporal correlations among multivariate time-series data with stackable STGAT networks. Meanwhile, a multi-scale input network is exploited to capture the temporal correlations in different time-scales. Experiments on a new wind turbine dataset (built and released by us) and three public datasets show that our method detects anomalies more accurately than baseline approaches and provide interpretability through observing the attention score among multiple sensors and different times.