The increasing frequency of extreme weather events has resulted in a rapid growth of unstructured meteorological texts, posing challenges for accurate disaster-related information extraction. Existing relation extraction models that integrate semantic and syntactic information via Graph Convolutional Networks (GCNs) often suffer from noise amplification and information redundancy. To address these limitations, we propose a domain-specific relation extraction framework that integrates Bidirectional Encoder Representations from Transformers (BERT) with an Adaptive Denoising Graph Network. A dual-tuning architecture is designed to jointly model semantic and syntactic features. Specifically, a Self-Attention Graph Convolutional Network (SA-GCN) dynamically prunes irrelevant dependency structures, while a Residual Shrinkage Network (RS-Net) performs fine-grained feature denoising through sample-adaptive threshold learning. Experiments on the public DUIE 2.0 dataset and a newly constructed Agricultural Meteorological Disaster dataset demonstrate that the proposed model achieves F1 scores of 91.51% and 92.84%, respectively, outperforming state-of-the-art methods. Ablation studies further confirm the effectiveness of adaptive denoising in handling complex linguistic structures in disaster reports. The proposed approach enhances the robustness and accuracy of meteorological relation extraction and provides technical support for knowledge graph construction and intelligent disaster early warning systems.