To achieve the automated grinding and polishing of the blade tip fillet in an aero-engine blade, a study on the micro-arc fillet grinding and polishing process based on elastic grinding tools was conducted, and a highly controllable method for machining the micro-arc fillet of the blade tip was proposed. An elastic grinding and polishing wheel with polyester fiber as the base material was employed. By leveraging the characteristic of elastic deformation of the grinding and polishing wheel during the machining process, the abrasive coated on the surface of the base material was used to grind and polish the blade tip apex angle into a micro-radius fillet. Based on the elastic contact theory and the Preston removal theory, the theoretical contact model and material removal model of the grinding and polishing wheel and the blade tip apex angle under the machining state were established. The Abaqus software was utilized to perform a simulation analysis of the stress in the contact region of the model and to simulate the removal distribution function. Theory proves that through the adaptive enveloping contact deformation between the elastic grinding and polishing wheel and the blade tip apex angle, a “micro-surface contact cutting” was formed between the machining region and the grinding and polishing wheel, enabling the machining of a micro-radius arc fillet. The fillet grinding and polishing experiment of the blade tip apex angle was carried out to verify the feasibility and controllability of achieving the micro-arc fillet machining. The results showed that the adaptive enveloping deformation of the elastic grinding and polishing wheel led to an arc-shaped stress distribution in the contact region of the blade tip, and the abrasive coated on the base material could effectively grind and polish to achieve the fillet machining. This machining method effectively realized the automated machining of the micro-arc fillet of the blade tip, with good consistency in dimensional accuracy and surface quality. The roughness Ra was stable between 0.20 μm and 0.28 μm, and the variation in the fillet radius was stable within a range of 16 μm.