Graph anomaly detection technology has broad applications in financial fraud and risk control. However, existing graph anomaly detection methods often face significant challenges when dealing with complex and variable abnormal patterns, as anomalous nodes are often disguised and mixed with normal nodes, leading to the coexistence of homophily and heterophily in the graph domain. Recent spectral graph neural networks have made notable progress in addressing this issue; however, current techniques typically employ fixed, globally shared filters. This 'one-size-fits-all' approach can easily cause over-smoothing, erasing critical high-frequency signals needed for fraud detection, and lacks adaptive capabilities for different graph instances. To solve this problem, we propose a Multi-Head Spectral-Adaptive Graph Neural Network (MHSA-GNN). The core innovation is the design of a lightweight hypernetwork that, conditioned on a 'spectral fingerprint' containing structural statistics and Rayleigh quotient features, dynamically generates Chebyshev filter parameters tailored to each instance. This enables a customized filtering strategy for each node and its local subgraph. Additionally, to prevent mode collapse in the multi-head mechanism, we introduce a novel dual regularization strategy that combines teacher-student contrastive learning (TSC) to ensure representation accuracy and Barlow Twins diversity loss (BTD) to enforce orthogonality among heads. Extensive experiments on four real-world datasets demonstrate that our method effectively preserves high-frequency abnormal signals and significantly outperforms existing state-of-the-art methods, especially showing excellent robustness on highly heterogeneous datasets.