The invention relates to a machine for cutting the tips of the leaves off agave plants and preparing the plants for the subsequent removal of the core. The machine is characterised in that it comprises a chassis defining a platform having: a rear end comprising a structural frame supporting arms that project rearwards, wheel rims that rest on the ground being secured to said arms a front end comprising a structural frame having arms extending frontwards, a tractor-coupled drawbar being secured to said arms and an arm that connects to the power take-off of the tractor and is secured in the upper part of the structural frame. The invention also comprises a supporting base which can slide under the action of hydraulic elements, is mounted on a pair of parallel rails and is arranged transversely across the platform. The supporting base is adapted to receive means for supporting and securing a folding and extending head structure for cutting the tips of the leaves off agave plants, compr ising a mechanism including lower pincers that are activated by hydraulic means and that clamp the agave plant and close so as to collect and cut the tips using an upper pincer provided with cutting blades. The aforementioned head comprises a hydraulic mechanism and system for adjusting the heights and closure diameter of the pincer system in order to adapt to different plant sizes. The machine includes a hydraulic system with control buttons or levers, actuated by the operator.La presente invención está referida a una máquina para despuntar las pencas de plantas de agave y prepararlas para su jimado posterior, caracterizada porque consta de un chasis que define una plataforma que posteriormente comprende un marco estructural como medio de soporte de brazos proyectados posteriormente en los que se fijan llantas de apoyo al piso y comprendiendo en el extremo frontal un marco estructural con brazos proyectados frontalmente en los que se sujeta una barra de tiro que se fija en un tractor y
