The mask of Darth Vader was fashioned after a skull, with blank spaces for eyes to imply the nonexistence of a soul. The mask of Kylo Ren is formed without a mouth because his is a character who cannot speak.
There are many possible ways in which he can't speak. It may be that he doesn't know how to express himself or even that he doesn't know what he wants to express; "I'm being torn apart," he says. Perhaps he is hiding something, which would be the case if he is some kind of double or undercover agent. Or it might be that someone is trying to not let him speak; he is being contained in some way (presumably by Snoke). He himself might also be trying to repress something (like the light), to not let it speak out of his mouth and his actions.
Visually, the mask looks something like a criminal's muzzle, something made to contain threats and danger. It suggests that Kylo Ren is a threat, which is in fact why he chooses to wear this mask: he wants to look like intimidating, like his grandfather before him. But his mask has less of a "crown" than Vader's did: he is less powerful. And where Vader's mask was about blankness, Ren's is about blocking. There was nothing for Vader to hide because he had all but killed all the good in himself, but Ren has much that he still tries to suppress.
Speaking of his mask leads me to think of his face. I commented before on the unique, well, mutilation that Kylo Ren receives during his battle with Rey: Star Wars has so much of chopping off hands and limbs but he just got some deep wounds and a sliced face. Now I see why the face is significant.
The face is vanity. The face is self-image and your level of comfort with the idea of how other people perceive you. Ren wore the mask to feel powerful and to intimidate others into thinking he was powerful. So when Rey cuts his face, that's showing that his true face is damaged and that he is aware that it's damaged. The vanity is marred. The bravado fades into shock. His self-image struggles, as it probably has before, as only anger (which he is so quick to cultivate) can heal. Unless he can finally accept that he is damaged--and that damage to the light is not good.
Oh, Kylo Ren, don't you see that even though you've fashioned this dark mask for yourself, you are constantly wanting to take off the mask and let your own face be free? This shroud of darkness is not the answer. If you continue down this path, you will have even more scars than the slash across your face. It's never too late to turn away, but now you're marked. Now your mask is not just there to intimidate: it is there to hide your weakness and decay, as visually represented by a deep scar.