A device for cutting a plate of a pre-determined thickness, preferably a glass plate, includes a frame; a support device for a cutting utensil, which is connected to the frame and adapted to have and upward and downward movement; and a hinged lever system, which has a feeler element and is kinematically coupable with the support device to bind it in a pre-determined initial position with respect to the frame. When the feeler element is pressed against a surface, the hinged lever system causes the support device with the cutting utensil to move downward from an initial position.