Embodied intelligence provides a promising paradigm for robotic machining systems, enabling autonomous perception, reasoning, and execution of diverse tasks via tight coupling of physical embodiment and decision-making. However, its industrial applications remain limited, as machining performance is highly constrained by robot physical properties and process conditions. Accordingly, this paper innovatively proposes an embodied intelligence control framework for hybrid robot machining systems. The framework decomposes complex machining tasks into three phases, including positioning, planning and manipulating. Driven by meta-skills, the framework realizes autonomous decision-making and execution. Considering the hybrid robot’s structural features, a realistic digital twin simulation environment is originally built based on a model-data-physics framework, realizing real-time simulation of key physical attributes to fully characterize the system’s physical state and support meta-skill learning. Moreover, a reinforcement learning method integrated with the strong constraints of the mechanistic models is proposed. By introducing reward functions and constraint conditions constructed based on the mechanistic models to guide the learning process, the efficiency and stability of learning are improved. Two representative meta-skills are developed through the method: workpiece clamping position selection and collision-free smooth trajectory planning. Finally, an embodied intelligent machining system is established and validated through milling tests on three workpieces with distinct geometric features, as well as a drilling task to assess adaptability to hardware configuration changes. The results demonstrate that the framework autonomously completes the full decision-making and execution without retraining, indicating the application potential of the proposed meta-skill-driven embodied intelligence framework for flexible manufacturing.