Recently, leveraging pre-training techniques to enhance point cloud models has become a hot research topic. However, existing approaches typically require full fine-tuning of pre-trained models to achieve satisfied performance on downstream tasks, accompanying storage-intensive and computationally demanding. To address this issue, we propose a novel Parameter-Efficient Fine-Tuning (PEFT) method for point cloud, called PointGST (Point cloud Graph Spectral Tuning). PointGST freezes the pre-trained model and introduces a lightweight, trainable Point Cloud Spectral Adapter (PCSA) to fine-tune parameters in the spectral domain. The core idea is built on two observations: 1) The inner tokens from frozen models might present confusion in the spatial domain; 2) Task-specific intrinsic information is important for transferring the general knowledge to the downstream task. Specifically, PointGST transfers the point tokens from the spatial domain to the spectral domain, effectively de-correlating confusion among tokens via using orthogonal components for separating. Moreover, the generated spectral basis involves intrinsic information about the downstream point clouds, enabling more targeted tuning. As a result, PointGST facilitates the efficient transfer of general knowledge to downstream tasks while significantly reducing training costs. Extensive experiments on challenging point cloud datasets across various tasks demonstrate that PointGST not only outperforms its fully fine-tuning counterpart but also significantly reduces trainable parameters, making it a promising solution for efficient point cloud learning. It improves upon a solid baseline by +2.28%, 1.16%, and 2.78%, resulting in 99.48%, 97.76%, and 96.18% on the ScanObjNN OBJ BG, OBJ OBLY, and PB T50 RS datasets, respectively. This advancement establishes a new state-of-the-art, using only 0.67% of the trainable parameters.