Graph anomaly detection is critical in domains such as healthcare and economics, where identifying deviations can prevent substantial losses. Existing unsupervised approaches strive to learn a single model capable of detecting both attribute and structural anomalies. However, they confront the tug-of-war problem between two distinct types of anomalies, resulting in suboptimal performance. This work presents TripleAD, a mutual distillation-based triple-channel graph anomaly detection framework. It includes three estimation modules to identify the attribute, structural, and mixed anomalies while mitigating the interference between different types of anomalies. In the first channel, we design a multiscale attribute estimation module to capture extensive node interactions and ameliorate the over-smoothing issue. To better identify structural anomalies, we introduce a link-enhanced structure estimation module in the second channel that facilitates information flow to topologically isolated nodes. The third channel is powered by an attribute-mixed curvature, a new indicator that encapsulates both attribute and structural information for discriminating mixed anomalies. Moreover, a mutual distillation strategy is introduced to encourage communication and collaboration between the three channels. Extensive experiments demonstrate the effectiveness of the proposed TripleAD model against strong baselines.