The Kuchisake-Onna will appear as a tall woman in a trench-coat with long, black hair. Her most telling feature is the surgical mask covering the bottom half of her face.
She will approach you and ask you a question: "Am I beautiful?"
If you reply, "No!" Your troubles are over. Mainly because she will produce a comically oversized pair of scissors and remove your head. Ah! You're thinking, So I'll answer "yes!" In which case she will remove her mask to reveal her grotesquely mutilated face, her smile sliced from ear to ear. "Am I still beautiful?" She will ask again.
If you have some kind of twisted Joker fetish and reply, "yes", she will take the aforementioned scissors, chase you down, and slice you in half. If you reply "no", she'll do it anyway. Some people just can't be satisfied.
If you don't fancy a haircut with too much off the top, your best bet is a neutral reply, such as "You're so-so", or "average". This will confuse the Split Mouth Woman, giving you just enough time to run like all the hounds of hell are at your heels (or in this case, a crazy bitch with a giant pair of scissors)