The clamping assembly includes a cutting insert with a lower passage housing a screw with a head for clamping the cutting insert against a bearing surface provided on a tool holder and comprising a screwing hole, wherein the screw head is shaped and arranged so as to press only on one side, with a flared opening, of the screw hole, the passage has a template incompatible with a template of the head in the clamping position, and, outside of the clamping, the cutting insert and the screw can change mutually relative positions so as to harmonize the two templates and thus release the cutting insert without having to entirely unscrew the screw.