Cutting device for processing product units

A device with a blade movable within an associated working space for cutting product units and with a conveying device in which the product units can be individually conveyed into the working space of the blade, wherein the conveying device comprises at least one two-part conveying channel associated with the blade, in which on one side first conveyor elements and on the other side second conveyor elements, which are assigned to one another in pairs, are guided, that the first and second conveyor elements each have a recess provided for partially receiving a separated product unit, and that the sides of the first and second conveyor elements which are facing one another, delimit therebetween the free working space, so that the blade is guidable within the working space in order to partially or completely cut a product unit held within the working space and held in the first and second conveyor elements which correspond to one another.