Drilling, cutting, and milling are the most common methods used in orthopedic surgery. However, popular machining methods do not obtain the complex shape of the periarticular tissue surfaces, increasing operation time and patient recovery. This paper reports an attempt to research a novel design of a machining process for surgical procedures. A device using abrasion machining based on mechanical erosion was proposed. Machining uses an undefined geometry of the cutting grains to cut tissue in any direction during oscillatory tool movement. This new concept is based on a cylindrical abrasive device made of brown fused alumina and silicon carbide grains deposited with an epoxy resin binder on the surface of a polyamide shaft. The best results in terms of machining efficiency were obtained for grains of the BFA80 type. Cutting experiments with different values in terms of cutting speed, granulation of the abrasive grains, pressure forces, and machining scope showed that the proposed concept, by developing the shape of the device, allows for penetration of the tissue structure. The research shows the possibility of using the proposed method during periarticular tissue machining.