The "mouth" of God is the manifestation, the operation of God's Laws; it is also the performance and preaching of His Holy Will, His Commandments, by the heralds, the preachers, the righteous.
The "mouth" of God is the symbol of His Messengers: the Patriarchs, the Prophets, Jesus Christ, the Apostles and all the Righteous, by whose good news (His Word) God "proclaims," "speaks," appeals to the mind and consciousness of man.
The "mouth" of God is also every man who, by his word and his pious way of life, testifies to those around him the Truth of God's Will revealed to him.
The "mouth" of Jesus Christ is His Apostles, His disciples, His followers, who proclaim the Will of God as expressed in His Gospel Teaching.
"The mouth" of a person is an expression of a person's righteous or sinful outlook and way of life.
Negative Meaning:
"The mouth of the dragon" is an image, a characteristic of the whole ideological system of the sinful world and the active servants of that system - its leaders, inspirers, spokesmen.
"The mouth of the beast..." - are the violent spokesmen for the politics and economics of the sinful system of the world-the servants of sinful ideological state systems and also their godless leaders, counselors, mentors, etc.
"The mouth of the False Prophet..." - is a false ideology, a sham, ceremonial religion in its various dogmatic, doctrinal varieties, forms, as well as pharisaical ministers of various false beliefs, religions, their ideologues, leaders, "teachers", "pastors", dignitaries, etc.
The "false lips" are people who spread "human precepts," i.e., traditions, false teachings, and beliefs, without knowing the true meaning of the scriptures.
"Blasphemous lips" are ungodly, vicious, impious men, denigrating the holiness of God's life-affirming Will, maligning His gracious Commandments, slandering the justice of God's Word, creating ideologies, dogmas, false teachings contrary to the Will of God, slandering and variously persecuting the holy way of life of the righteous