Dexterous grasping remains a fundamental yet challenging problem in robotics. A general-purpose robot must be capable of grasping diverse objects in arbitrary scenarios. However, existing research typically relies on restrictive assumptions, such as single-object settings or limited environments, showing constrained generalization. We present DexGraspVLA, a hierarchical framework for robust generalization in language-guided general dexterous grasping and beyond. It utilizes a pre-trained Vision-Language model as the high-level planner and learns a diffusion-based low-level Action controller. The key insight to achieve generalization lies in iteratively transforming diverse language and visual inputs into domain-invariant representations via foundation models, where imitation learning can be effectively applied due to the alleviation of domain shift. Notably, our method achieves a 90+% dexterous grasping success rate under thousands of challenging unseen cluttered scenes. Empirical analysis confirms the consistency of internal model behavior across environmental variations, validating our design. DexGraspVLA also, for the first time, simultaneously demonstrates free-form long-horizon prompt execution, robustness to adversarial objects and human disturbance, and failure recovery. Extended application to nonprehensile grasping further proves its generality.