In densely cluttered environments, physical interference, visual occlusions, and unstable contacts often cause direct dexterous grasping to fail, while aggressive singulation strategies may compromise safety. Enabling robots to adaptively decide whether to clear surrounding objects or directly grasp the target is therefore crucial for robust manipulation. We propose AdaClearGrasp, a closed-loop decision-execution framework for adaptive clearing and zero-shot dexterous grasping in densely cluttered environments. The framework formulates manipulation as a controllable high-level decision process that determines whether to directly grasp the target or first clear surrounding objects. A pretrained vision-language model (VLM) interprets visual observations and language task descriptions to reason about grasp interference and generate a high-level planning skeleton, which invokes structured atomic skills through a unified action interface. For dexterous grasping, we train a reinforcement learning policy with a relative hand-object distance representation, enabling zero-shot generalization across diverse object geometries and physical properties. During execution, visual feedback monitors outcomes and triggers replanning upon failures, forming a closed-loop correction mechanism. To evaluate language-conditioned dexterous grasping in clutter, we introduce Clutter-Bench, the first simulation benchmark with graded clutter complexity. It includes seven target objects across three clutter levels, yielding 210 task scenarios. We further perform sim-to-real experiments on three objects under three clutter levels (18 scenarios). Results demonstrate that AdaClearGrasp significantly improves grasp success rates in densely cluttered environments. For more videos and code, please visit our project website: https://chenzixuan99.github.io/adaclear-grasp.github.io/.