<p>Silicon nitride (Si₃N₄) is a high-performance ceramic with wide strategic applications in aerospace and thermal-shock environments, owing to its exceptional hardness, thermal stability, and fracture toughness. However, such superior properties render Si₃N₄ extremely difficult to machine, with limited techniques available that provide good surface quality and a high material removal rate (MRR). This work proposes a novel dual-hybrid machining approach for drilling Si₃N₄, termed chemically assisted rotary machining with an ultrasonically vibrated workpiece (CRUWM), which is based on a ductility-dominated ductile–brittle regime mechanism with chemical assistance. In the present approach, ultrasonic vibrations are applied to the workpiece, resulting in distinct mechanical and material removal advantages. In addition, a methanol-based chemically active medium is used to induce a chemo-mechanical effect that suppresses brittle fracture. Substantial improvements in responses, including hole profile accuracy, surface finish, cutting forces, and MRR, are demonstrated in comparison to popular rotary ultrasonic machining (RUM). The experimental results reveal a 75.9% reduction in hole taper angles, a 34.3% decrease in surface roughness (Ra), a 29.9% reduction in cutting forces, and a 92.9% increase in MRR. A comprehensive analysis of the underlying material removal mechanisms is presented, elucidating the synergistic effects of workpiece-excited ultrasonics and chemical assistance on machinability enhancement. The proposed CRUWM approach demonstrates a transformative and cost-effective route for the precise machining of Si₃N₄, enabling superior surface integrity and geometric accuracy for extreme manufacturing applications.</p>