Detecting harmful memes is critical for maintaining safe online communities. However, harmful intent is often implicit, arising from visual–textual incongruity and cultural stereotypes, which challenges existing multimodal detectors. We propose SyRHM, a framework that decomposes harmful meme detection into meaning-grounded retrieval and symbolic-language-enhanced multi-stage reasoning. SyRHM retrieves semantically related memes by parsing multimodal content into textual elements and description, providing grounded context beyond surface-level similarity. Building on the retrieved context, SyRHM uses a translator stage to convert multimodal inputs into symbolic intermediate representations, and then performs multi-stage reasoning via planner and solver stages, enabling expressive and interpretable analysis of harmful intent. Experiments on FHM, HarM, and MultiOff show that SyRHM consistently outperforms multimodal and reasoning-based baselines, while providing reasoning traces for harmful content. The code is available at: https://anonymous.4open.science/r/SyRHM-CC46