Silicon nitride (Si3N4) is a critical advanced ceramic used in high-performance applications, but its inherent hardness and brittleness make it difficult to machine. Conventional methods like rotary ultrasonic machining (RUM) often result in subsurface damage and limited efficiency. This paper introduces a novel process, chemically-assisted rotary ultrasonic workpiece machining (CRUWM), designed to overcome these challenges. The key innovation lies in imparting ultrasonic vibrations directly to the workpiece while using methanol as a chemically-active fluid. This configuration leverages the Rehbinder effect to induce an absorption-induced reduction in the material's strength at the machining interface, transitioning the material removal mechanism from pure brittle fracture to a more favourable ductile-brittle hybrid mode. The results demonstrate the superiority of the CRUWM process over conventional RUM. We achieved a 75.9% reduction in hole taper angle, a 34.3% decrease in surface roughness (Ra), a 29.9% reduction in cutting forces, and a remarkable 92.9% increase in the material removal rate (MRR). These findings present a cost-effective and highly efficient pathway for precision machining of silicon nitride and other hard-to-machine ceramics.