Graph neural networks (GNNs) have achieved remarkable success in various domains, yet they often struggle with domain adaptation due to significant structural distribution shifts and insufficient exploration of transferable patterns. One of the main reasons behind this is that traditional approaches do not treat global and local patterns discriminatingly so that some local details in the graph may be violated after multi-layer GNN. Our key insight is that domain shifts can be better understood through spectral analysis, where low-frequency components often encode domain-invariant global patterns, and high-frequency components capture domain-specific local details. As such, we propose FracNet (\underline{\textbf{Fr}}equency \underline{\textbf{A}}ware \underline{\textbf{C}}ontrastive Graph \underline{\textbf{Net}}work) with two synergic modules to decompose the original graph into high-frequency and low-frequency components and perform frequency-aware domain adaption. Moreover, the blurring boundary problem of domain adaptation is improved by integrating with a contrastive learning framework. Besides the practical implication, we also provide rigorous theoretical proof to demonstrate the superiority of FracNet. Extensive experiments further demonstrate significant improvements over state-of-the-art approaches.