does the circuit have to include the actual cutter, for example a hotwire?
i image a decade counter could be used to sequence the events, eg when the rubber meets the photocell, it generates a pulse, the belt stops, cutter engages, the limit switch on the cutter sends a pulse, the cutter retracts, when the cutter hits the start of travel switch, a pulse i generated, the rubber is pushed off the belt, causeing a pulse from the photocell, which resets the counter
sorry for my bad description - im not a technical person.
i would use a pic, but then again pics are soo cheap i used them for everything - im a digital person stuck in an analogue world