Abstract: The present invention relates to a cutting insert applicable to machining tools and the tool bearing it. The insert (1) has a cutting edge (12) which can be completely sharp or can have a rounding between R=0.030 mm and 0.050 mm, with an angle of impact (123) between 68° and 90° in both cases, and a rounded chip breaker (13), both arranged in a layer of polycrystalline diamond (PCD) (11) at least 1 mm thick covering the entire cutting surface of the insert (1). The tool includes a body (2) formed by a core (22) coupleable to the machining center, said core externally bearing a perimetral sleeve (21) housing the cutting inserts (1), with the layer of PCD (11) thereof being in direct contact with the sleeve (21). The invention may include a hydraulic system (23) between the sleeve (21) and the core (22).