In a tool for tightening clamps, of the kind comprising a flexible strip and an apertured head, having a passage in which the end of the flexible strip can be engaged after the strip has been passed around a bunch of articles to be clamped together and through the apertured head, the tool being used to cut-off that portion of the flexible strip of the clamp which projects beyond the apertured head following tightening to a greater or lesser degree of the clamp around the articles, the improvement comprising a displacement member, a trigger and coupling means including a swinging link provided between the displacement member and the trigger and including a sudden release mechanism comprising a cam having a cam surface with two separate stable zones separated from one another by an unstable zone and a cam-follower maintained in contact with the cam surface of the cam, the cam and the cam-follower being relatively movable to swing said cutting lever from a rest position into a working position, one of the cam and the cam-follower being fixed to a trigger and the other being provided on a swinging link of the coupling means provided between the trigger and the displacement member, elastic calibrating means coupled to the swinging link and engagement means for the swinging link engaged with complementary engagement means fixed to the cutting lever. Preferably the cam is formed on the swinging link and the swinging link is formed to define a heart-shaped hole, opposite sides of which hole define the stable zones of the cam surface and the cam-follower comprises a pin integral with the trigger and engaged in the heart-shaped hole.