Adapting pretrained multi-modal models to evolving test-time distributions, known as multi-modal test-time adaptation, presents a significant challenge. Existing methods frequently encounter negative transfer in the unbiased modality and catastrophic forgetting in the biased modality. To address these challenges, we propose Decoupling Adaptation for Stability and Plasticity (DASP), a novel diagnose-then-mitigate framework. Our analysis reveals a critical discrepancy within the unified latent space: the biased modality exhibits substantially higher interdimensional redundancy (i.e., strong correlations across feature dimensions) compared to the unbiased modality. Leveraging this insight, DASP identifies the biased modality and implements an asymmetric adaptation strategy. This strategy employs a decoupled architecture where each modality-specific adapter is divided into stable and plastic components. The asymmetric mechanism works as follows: for the biased modality, which requires plasticity, the plastic component is activated and updated to capture domain-specific information, while the stable component remains fixed. Conversely, for the unbiased modality, which requires stability, the plastic component is bypassed, and the stable component is updated using KL regularization to prevent negative transfer. This asymmetric design enables the model to adapt flexibly to new domains while preserving generalizable knowledge. Comprehensive evaluations on diverse multi-modal benchmarks demonstrate that DASP significantly outperforms state-of-the-art methods.