Anomaly detection in graph data has gained significant attention, especially in detecting anomaly subgraphs, which is crucial for applications like disease outbreak detection, financial fraud detection, and network security. However, existing methods often focus on single-layer networks and struggle to handle multi-layer networks with correlated anomalies. To address this, we propose ASMAN (Anomaly Aligned Subgraphs Detection on Multi-Layer Attributed Networks), a novel framework that integrates deep learning-based anomaly detection with network alignment algorithms. ASMAN effectively detects and aligns anomaly subgraphs across different network layers by maximizing the anomaly scores and alignment scores of anomaly sungraph pairs. Extensive experiments on both synthetic and real-world datasets validate the effectiveness and efficiency of our work. ASMAN increased cross-layer connections by at least 50% compared to the best baseline, while maintaining high anomaly detection performance. The research on the NSF dataset had successfully identified influential awards and article groups. This work fills a crucial gap in detecting aligned anomaly subgraphs in multi-layer static attributed networks.