It would not be legal or ethical for most websites. But HN might be different, because it doesn't try to make money (so you aren't depriving it of anything tangible by rehosting its content), and it has a public API that includes stories (you should use it, of course) that doesn't mention anything about republishing content being forbidden, or say that it's limited to personal use.

Hopefully an HN moderator or similar will know the answer and reply here. If they don't, you should email HN.