The machine has two identical cutting assemblies (A, B) with a pile of circular cutting tools. Each tool has a carrier disk (15) with peripheral tooth, where the disk carries a cut toothed crown (16) of corresponding profile at its periphery. The tools are piled so as to constitute the two assemblies in a manner that their crowns are arranged facing each other. The assemblies are positioned on top with respect to each other so that spacing between the crowns is adjustable and is between 1 and 10 mm to position vine shoot.
