Multiplex graphs are widely used to model multi-relational complex systems and play an important role in various real-world scenarios, such as financial systems and social networks. Hence, detecting anomalous samples in multiplex graph becomes crucial to ensure cybersecurity and stability. Although existing homogeneous graph anomaly detection (GAD) methods can be applied to deal with multiplex graphs, they still face two major challenges: 1) Due to the multiplicity and complexity of relations in multiplex graphs, homogeneous GAD models fail to effectively capture anomalous behaviors that correlate with diverse relational patterns. 2) In real-world applications, malicious entities usually disguise themselves through various camouflage strategies, making it difficult to capture subtle anomalous features via single-relation analysis. To address these challenges, we propose a novel unsupervised anomaly detection method for multiplex graphs based on Similarity-constrained Fusion Graph Autoencoder (SFGA). In SFGA, we design a multiplex graph autoencoder and introduced a cross-plex attention module at the model bottleneck to achieve comprehensive modeling of cross-relation anomaly patterns. Then, a similarity balancing strategy is proposed to constrain node representations at the bottleneck from both local and global perspectives, enhancing the discriminative power against camouflaged anomalies of autoencoder and enabling more effective identification of anomalous nodes with overlapping or deceptive patterns. Extensive experiments are conducted on both synthetic and real-world datasets at varying scales, and the results demonstrate that our proposed method outperforms state-of-the-art approaches by a large margin.