A method is disclosed for severing a continuous reinforcement from a print head at conclusion of an event during fabrication of a composite structure. The method may include moving the print head a distance away from the composite structure that provides clearance for a cutting mechanism between an outlet of the print head and the composite structure, and responsively causing the cutting mechanism to make a first cut of the continuous reinforcement at a boundary of the composite structure. The method may also include moving the print head to a waste discard location, and responsively causing the cutting mechanism to make a second cut of the continuous reinforcement at a desired distance offset from the outlet of the print head.