A hand-held power tool having a motor, a cutting member and a transmission linking the cutting member to the motor, the motor and the transmission being housed in a main housing, the transmission having a ball screw/nut mechanism with a screw and a nut, one of the screw and the nut being rotatably engaged with the motor, and the other of the screw and the nut being linked to the cutting member. The tool has a protective housing for protecting the ball screw/nut mechanism, separate from the main housing, and a sliding seal cooperating with an inner face of the protective housing, the sliding seal being driven by one of the nut and the screw linked to the cutting member, the sliding seal being rigidly connected respectively to one of a sleeve covering the nut and a cap protecting the screw.