Graph Contrastive Learning (GCL) has demonstrated remarkable effectiveness in learning representations on graphs in recent years. To generate ideal augmentation views, the augmentation generation methods should preserve essential information while discarding less relevant details for downstream tasks. However, current augmentation methods usually involve random topology corruption in the spatial domain, which fails to adequately address information spread across different frequencies in the spectral domain. Our preliminary study highlights this issue, demonstrating that spatial random perturbations impact all frequency bands almost uniformly. Given that task-relevant information typically resides in specific spectral regions that vary across graphs, this one-size-fits-all approach can pose challenges. We argue that indiscriminate spatial random perturbation might unintentionally weaken task-relevant information, reducing its effectiveness. To tackle this challenge, we propose applying perturbations selectively, focusing on information specific to different frequencies across diverse graphs. In this paper, we present GASSER, a model that applies tailored perturbations to specific frequencies of graph structures in the spectral domain, guided by spectral hints. Through extensive experimentation and theoretical analysis, we demonstrate that the augmentation views generated by GASSER are adaptive, controllable, and intuitively aligned with the homophily ratios and spectrum of graph structures.