In most cases, "mouth" in the Bible represents thought and logic, especially the kind of active, concrete thought that is connected with speech. The reason for this is pretty obvious, but it also holds when people, for instance, remove a stone from the mouth of a well, which represents gaining access to spiritual ideas. The mouth is used for eating as well as speaking, of course. In those circumstances, it represents our first, most external perception of a new spiritual idea or desire. This also makes sense, mirroring the way tasting food in the mouth gives us an instant impression of the quality of the food.

'Skins' or 'hides' signify external things, because the hide is the outermost organ of an animal where its interiors extend, the same as with a person's dermis or skin. 'Skin' corresponds to truth or to falsity in the extremes. See Arcana Coelestia 1835, 10036, and Apocalypse Explained 386. 'Skin,' as in Job 19:26, means the natural degree a person has with him after death.

In Exodus 22:27, this signifies things that are relatively external. (Arcana Coelestia 9215)

In Exodus 34:29, this signifies the internal of the Word shining from the external. (Arcana Coelestia 10691)

In Job 19:20, this signifies being not entirely in falsities. (Apocalypse Explained 556[11])

In Jeremiah 13:23, this signifies that evil cannot change its nature. (Apocalypse Explained 780[5])

In Genesis 3:21, this signifies that the Lord instructed them in spiritual and natural good. (Arcana Coelestia 292)

In Genesis 27:16, this signifies the external truths of domestic good. (Arcana Coelestia 3540)