It definitely has a mouth, it's just that maybe you can't see it. And I've read in some science books before that snails not only have mouths, but also teeth.
The snail's mouth is said to be under the two tentacles on top of its head. (With all due respect, I always thought those were the snail's eyes). So, the snail usually feeds through its mouth. As for how it eats, I don't quite understand.
When I was a kid, I used to like catching snails for fun, and sometimes I'd catch them to watch them eat vegetables. But now that I've grown up, I suddenly realized that the number of snails in the city is quite small, and I don't even feel like I've seen snails for a long time.