A cutting tool including a tool body with an insert seat and an associated clamp pocket, a cutting insert releasably mountable in the insert seat, a clamp received in the clamp pocket and a screw that extends with play through a through hole in the clamp and is engaged in a hole at the bottom of the clamp pocket, is provided. Upon tightening of the screw, the clamp will slide against an inclined guide surface in the slide pocket via a slide surface on the clamp, which will force the clamp to move transversally to the screw shaft towards the cutting insert such that a clamp protrusion on the clamp is moved into a recess in the cutting insert and clamping surfaces on the clamp are pressed tightly against corresponding contact surfaces on the cutting insert.