In a medium bowl, whisk together the mayonnaise, mustard, cayenne, sugar, celery seed, apple cider vinegar, and salt and black pepper, to taste, until thoroughly combined. Reserve.
Using a large holed grater attachment for a food processor, grate the cabbage, carrots, red onion, sweet potato, and apples. Remove to a large serving bowl and toss with the reserved dressing. Cover with plastic wrap and refrigerate for at least 2 hours.