Semantic segmentation of multi-modal remote sensing imagery plays a pivotal role in land use/land cover (LULC) mapping, environmental monitoring, and precision earth observation. Current multi-modal approaches mainly focus on integrating complementary visual modalities (e.g., optical and synthetic aperture radar (SAR) imagery), yet neglect the incorporation of non-visual textual data. To address this limitation, we propose TSMNet, a text supervised multi-modal open vocabulary semantic segmentation network that synergistically integrates textual supervision with visual representation for open-vocabulary semantic segmentation. Unlike conventional multi-modal segmentation frameworks, TSMNet introduces a dual-branch text encoder to extract both scene-level semantic and object-level label information from various textual data, enabling dynamic cross-modal fusion. These text-derived features dynamically interact with visual embeddings through the proposed text-guided visual semantic fusion module, enabling domain-aware feature refinement and human-interpretable decision-making. Moreover, integrating text opens pathways for open-vocabulary semantic segmentation, enabling systems to dynamically segment targets through natural language descriptions, thereby overcoming the rigid constraints of traditional pre-defined classification heads. To verify our method, we innovatively construct two new multimodal datasets, and carry out extensive experiments to make a comprehensive comparison between the proposed method and other state-of-the-art (SOTA) semantic segmentation models. Results demonstrate that TSMNet achieves superior segmentation accuracy while exhibiting robust generalization capabilities across diverse geographical and sensor-specific scenarios. The source code will be available at <code>https://github.com/yeyuanxin110/TSMNet</code>.