Multi-modal affective computing aims to automatically recognize and interpret human attitudes from diverse data sources such as images and text, thereby enhancing human-computer interaction and emotion understanding. Existing approaches typically rely on unimodal analysis or straightforward fusion of cross-modal information that fail to capture complex and conflicting evidence presented across different modalities. In this paper, we propose a novel LLM-based approach for affective computing that explicitly deconstructs visual and textual representations into shared (modality-invariant) and modality-specific components. Specifically, our approach firstly encodes and aligns input modalities using pre-trained multi-modal encoders, then employs a representation decomposition framework to separate common emotional content from unique cues, and finally integrates these decomposed signals via an attention mechanism to form a dynamic soft prompt for a multi-modal LLM. Extensive experiments on three representative tasks for affective computing, namely, multi-modal aspect-based sentiment analysis, multi-modal emotion analysis, and hateful meme detection, demonstrate the effectiveness of our approach, which consistently outperforms strong baselines and state-of-the-art models.