Tool-holding device (11) for a machining tool, comprising: a tool-holder body (13); a receiving part (15) defined in the tool-holder body (13); a retaining element (17) provided with a pair of mutually cooperating jaws (17a,17b); a female seat (19) between the jaws for an engaging male portion (21) of a machining tip (23), the jaws (17a,17b) being capable of taking a locking configuration, in which the engaging portion (21) of the tool (23) is firmly locked within the seat (19) of the retaining element (17), and a disengaged configuration in which the engaging portion (21) of the tip (23) can be detached from the retaining element (17); a moveable component (25) which bear the main load of holding the retaining element (17) in the receiving part (15) when the retaining element (17) is in the configuration in which it engages the tool (23).