Mixture-of-Experts (MoE) architectures in large language models (LLMs) achieve exceptional performance, but face prohibitive storage and memory requirements. To address these challenges, we present $D^2$-MoE, a new delta decompression compressor for reducing the parameters of MoE LLMs. Based on observations of expert diversity, we decompose their weights into a shared base weight and unique delta weights. Specifically, our method first merges each expert's weight into the base weight using the Fisher information matrix to capture shared components. Then, we compress delta weights through Singular Value Decomposition (SVD) by exploiting their low-rank properties. Finally, we introduce a semi-dynamical structured pruning strategy for the base weights, combining static and dynamic redundancy analysis to achieve further parameter reduction while maintaining input adaptivity. In this way, our $D^2$-MoE successfully compact MoE LLMs to high compression ratios without additional training. Extensive experiments highlight the superiority of our approach, with over 13% performance gains than other compressors on Mixtral|Phi-3.5|DeepSeek|Qwen2 MoE LLMs at 40$\sim$60% compression rates. Codes are available in https://github.com/lliai/D2MoE.