Transformer-based large-scale pre-trained models achieve great success, and fine-tuning, which tunes a pre-trained model on a task-specific dataset, is the standard practice to utilize these models for downstream tasks. Recent work has developed adapter-tuning, but these approaches either still require a relatively high resource usage. Through our investigation, we show that each adapter in adapter-tuning does not have the same impact on task performance and resource usage. Based on our findings, we propose SAFE, which gradually freezes less-important adapters that do not contribute to adaptation during the early training steps. In our experiments, SAFE reduces memory usage, computation amount, and training time by 42.85\%, 34.59\%, and 11.82\%, respectively, while achieving comparable or better performance compared to the baseline. We also demonstrate that SAFE induces regularization effect, thereby smoothing the loss landscape.