If you want to shred cabbage in a food processor, the first thing you need to do is cut the cabbage into quarters. Then, place the quarters in the food processor with the cutting blade attached. Pulse the food processor until the cabbage is shredded to your desired consistency. You may need to stop and scrape down the sides of the bowl a few times during this process. Once your cabbage is shredded, you can use it in any recipe that calls for shredded cabbage or coleslaw mix.