This invention refers to an improved foldable and extensible head for agave harvest, characterized by including a vertical structure in whose lower end there is a support and fixation element of a lower-cut clamp, to cut the agave plant from its base, defined by a pair of straight-cut blades in a couple of curved clamps, completely opposing each other, each one fixed with its own rotating axis on the aforementioned support and fixation element. Each clamp includes a circular or semi-circular gear that allows the interlocking of both clamps and that together define a zipper mechanism to accurately synchronize the closing and opening movement between the clamps; a fixation structure of at least one hydraulic or pneumatic actuator is assembled in the rear area of the aforementioned support and fixation element, where the stem is pivotally fixed in the rear part, next to the rotating axis of at least one curved clamp to close or open both clamps as a result of the abovementioned zipper mechanism.