In unstructured environments, functional dexterous grasping calls for the tight integration of semantic understanding, precise 3D functional localization, and physically interpretable execution. Modular hierarchical methods are more controllable and interpretable than end-to-end VLA approaches, but existing ones still rely on predefined affordance labels and lack the tight semantic--pose coupling needed for functional dexterous manipulation. To address this, we propose BLaDA (Bridging Language to Dexterous Actions in 3DGS fields), an interpretable zero-shot framework that grounds open-vocabulary instructions as perceptual and control constraints for functional dexterous manipulation. BLaDA establishes an interpretable reasoning chain by first parsing natural language into a structured sextuple of manipulation constraints via a Knowledge-guided Language Parsing (KLP) module. To achieve pose-consistent spatial reasoning, we introduce the Triangular Functional Point Localization (TriLocation) module, which utilizes 3D Gaussian Splatting as a continuous scene representation and identifies functional regions under triangular geometric constraints. Finally, the 3D Keypoint Grasp Matrix Transformation Execution (KGT3D+) module decodes these semantic-geometric constraints into physically plausible wrist poses and finger-level commands. Extensive experiments on complex benchmarks demonstrate that BLaDA significantly outperforms existing methods in both affordance grounding precision and the success rate of functional manipulation across diverse categories and tasks. Code will be publicly available at https://github.com/PopeyePxx/BLaDA.