A hatchet has a large head on a skinny body; the head is usually longer than it is tall, and very thin. One edge is sharp and the other is not.
None of these features, much less all of them, apply to any human head or face I could name. But "hatchet-faced" is a nearly cliche descriptor for people of otherwise nondescript natures.
A Google image search yields one exceedingly popular result:
|Could this face chop wood? Maybe. But it wouldn't be my first choice.|
After the first page or so of search results, random ordinary faces start coming up. I, personally, can't pick out anything unusual or particularly common among them. They are not particularly beautiful or ugly as a whole, but the "hatchet-faced" connection tells me that they don't show up in the search because someone wants to show how pretty they are.
So you have to wonder, how the hell did this phrase come about? I have no freaking clue, and not much interest in finding out. I do have a guess as to how it is perpetuated, though: it's a simple, common, and easily communicated way of calling someone "ugly" without using such offensive language. Most people wouldn't think of a hatchet as a particularly beautiful or elegant thing, after all - they'd be wrong, in my opinion, but that's another story. That aside, likening someone's face to a mundane tool, like a hammer or a buzz saw, is probably not at all flattering to say the least.
Is this cliche a lazy piece of poetic language that is not actually meaningful except as code for "ugly"? If not, what does it actually mean? I say it means nothing, so don't be lazy. Some dictionaries say it means "a narrow face with sharp features" but I think that's misleading as well, especially considering the variety of faces the phrase is applied to in Google Images.
Incidentally, a quick search on my kindle for the phrase "hatchet-faced" yielded six books by four authors, including some Robert Jordan and even Stephen King. I'm fairly sure that it also came up in both of the Monster Hunter books I read recently. It's not just my imagination then, especially if the phrase is in online dictionaries (and my kindle dictionary as well). I certainly don't have to agree, though.