Multimodal Sentiment Analysis (MSA) aims to infer human sentiment by integrating information from multiple modalities such as text, audio, and video. In real-world scenarios, however, the presence of missing modalities and noisy signals significantly hinders the robustness and accuracy of existing models. While prior works have made progress on these issues, they are typically addressed in isolation, limiting overall effectiveness in practical settings. To jointly mitigate the challenges posed by missing and noisy modalities, we propose a framework called Two-stage Modality Denoising and Complementation (TMDC). TMDC comprises two sequential training stages. In the Intra-Modality Denoising Stage, denoised modality-specific and modality-shared representations are extracted from complete data using dedicated denoising modules, reducing the impact of noise and enhancing representational robustness. In the Inter-Modality Complementation Stage, these representations are leveraged to compensate for missing modalities, thereby enriching the available information and further improving robustness. Extensive evaluations on MOSI, MOSEI, and IEMOCAP demonstrate that TMDC consistently achieves superior performance compared to existing methods, establishing new state-of-the-art results.