Effectively mining anomalous subgraphs in networks is crucial for various applications, including disease outbreak detection, financial fraud detection, and activity monitoring in social networks. However, identifying anomalous subgraphs poses significant challenges due to their complex topological structures, high-dimensional attributes, multiple notions of anomalies, and the vast subgraph space within a given graph. Classical shallow models rely on handcrafted anomaly measure functions, limiting their applicability when prior knowledge is unavailable. Deep learning-based methods have shown promise in detecting node-level, edge-level, and graph-level anomalies, but subgraph-level anomaly detection remains under-explored due to difficulties in subgraph representation learning, supervision, and end-to-end anomaly quantification. To address these challenges, this paper introduces a novel deep framework named Anomalous Subgraph Autoencoder (AS-GAE). AS-GAE leverages an unsupervised and weakly supervised approach to extract anomalous subgraphs. It incorporates a location-aware graph autoencoder to uncover anomalous areas based on reconstruction mismatches and introduces a supermodular graph scoring function module to assign meaningful anomaly scores to subgraphs within the identified anomalous areas. Extensive experiments on synthetic and real-world datasets demonstrate the effectiveness of our proposed method.