The invention relates to a plant grafting machine (1) and method, the machine being provided for performing automatic grafos, including a means for holding plant stalks and a means for cutting said stalks, and a grafting means for joining the cut stalks, by means of a clamp (11) provided by a grafting unit. The holding means includes two mutually opposed runners that can move axially by means of an actuator means, said runners (4,5) being associated with the cutting means in order to made a bevel cut and, when viewed from above, said runners are offset on two parallel axes such that, during the grafting process, said two cut stalks are mutually aligned. Said grafting means includes an continuous supply belt from which the clamp (11) is obtained, a secondary cutting means for forming the clamp (11), and a placement means located in front of the supply belt for placing the clamp.
