Recent studies have demonstrated that many layers are functionally redundant in large language models (LLMs), enabling model compression by removing these layers to reduce inference cost. While such approaches can improve efficiency, indiscriminate layer pruning often results in significant performance degradation. In this paper, we propose GRASP (Gradient-based Retention of Adaptive Singular Parameters), a novel compression framework that mitigates this issue by preserving sensitivity-aware singular values. Unlike direct layer pruning, GRASP leverages gradient-based attribution on a small calibration dataset to adaptively identify and retain critical singular components. By replacing redundant layers with only a minimal set of parameters, GRASP achieves efficient compression while maintaining strong performance with minimal overhead. Experiments across multiple LLMs show that GRASP consistently outperforms existing compression methods, achieving 90% of the original model's performance under 20% compression ratio.