The equipment is made to give way to the needs of the small assembling companies or for the cutting of cut down chains and also for cutting chains in small series. After having inserted one end of the chain into the cutting system, the operator pulls the same end to a defined point fixed on the millimetered scale. At this point, activating the pneumatic valve, a cylinder positions the chain stich on the cutting point and immediately advances a punch with pneumatic pulling that partially expels the pivot of the chain. The depth of expulsion of the pivot is adjustable. There is either a partial expulsion of one pin of total expulsion of two pins.