Cutting red cabbage for coleslaw is fairly simple. Here's how to do it: Remove the outer leaves of the red cabbage and discard them. First cut the head of cabbage in half, from the stem to the top. Cut each half in half again, so you have four quarters of cabbage. Cut out the tough stem at the bottom of each quarter. Slice each quarter of cabbage as thinly as possible with a sharp knife. You can also use a mandoline or food processor with a slicing blade to achieve even thinner slices.