That is not an exit.
I heard that Mt. Fuji has a secret entrance and exit.
This baseball stadium’s exit is over there.
The mouth you exit out of is just a doorway (I hope), but an easier way to describe this word or concept is to call it an exit.
This is a jukugo word, which usually means on'yomi readings from the kanji. 出口 is an exception to this rule, however, and uses its kun'yomi readings. There's no particular reason why this is, but oftentimes a "body part" word (like mouth) changes a word to use kun'yomi readings instead of on'yomi ones. You already know the kun'yomi reading for 口 (くち) from learning the vocab, but to remember the reading for 出 you can think the following:
If I exit out this mouth, I'll end up in the ocean (you were swallowed by a whale) and I will surely end up dead (で).
Also keep in mind that because of rendaku, くち becomes ぐち.