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.

701. 16:13 And I saw coming out of the mouth of the dragon, out of the mouth of the beast, and out of the mouth of the false prophet. This symbolizes something perceived from a theology founded on the doctrine of a trinity of persons in the Godhead and on the doctrine of justification by faith alone apart from works of the law.

A mouth symbolizes doctrine, and preaching and discourse from it (nos. 454, 574). The dragon symbolizes an acknowledgment of three gods and of justification by faith alone, and so a destruction of the church (no. 537). The beast from the sea, which is the beast meant here, symbolizes people of the external church who are caught up in that acknowledgment and faith (nos. 567, 576, 577, 601). The false prophet symbolizes people of the internal church, who teach a theology founded on those doctrines. The false prophet has not been mentioned by that name before, but it is the beast from the earth that is called that now (see no. 594 above).

Now because all of this is symbolically meant by the dragon, the beast, and the false prophet (who is the beast from the earth here), it follows that John's seeing something coming out of the mouth of the dragon, out of the mouth of the beast, and out of the mouth of the false prophet, symbolizes something perceived from a theology founded on the doctrine of a trinity of persons in the Godhead and on the doctrine of justification by faith alone apart from works of the law.