Recent years, a dental implant surgery has been focused and has been widely prevalent. At present, the limited doctor had acquired the skill for the surgery. It is because of that the dental implant surgery has risks of an accident. Therefore, the high quality skill for the surgery is required. A dental hand-piece (dental drill) is used to make the hole which is for insertion of an artificial tooth root. The wear of drill makes the surgery more difficult and it increases the risks of accident. It is because an exact and safe operation is disturbed by wear of drill. To prevent the accidents, an monitoring technology of a cutting force and a cutting power is desired. In this paper, a cutting power estimation system is proposed. The proposed system achieves the estimation of the cutting power without a torque sensor and a force sensor. To estimate the cutting power, dynamics of two-dimensional cutting based on a cutting theory in a manufacturing industry is introduced. A measurement of cutting force is achieved by disturbance observer (DOB). In the experiment, an evaluation of the drill wear is tried as one of the applications of the proposed method.