If you call someone hatchet-faced, you are saying their face is long, thin, and sharp, as if the bones were cut with a hatchet — a narrow jaw, a hard line of a nose, little softness in the cheeks. It is about shape, not about whether the person is cruel or angry. Though actually, writers often hang the word on a character they want you to find a little frightening or hungry-looking, so the unkind feeling travels with it. You meet it in books more than in kind conversation. It is old-fashioned now, a little literary, and it lands as a cold description. You would not say it to a classmate’s face unless you meant to sting.