Consider a Warlock with The Great Old One patron and Pact of the Chain, who is mute because his tongue has been removed. He communicates with most characters through Awakened Mind, granted by the Great Old One.
The invocation Voice of the Chain Master says:
Voice of the Chain Master
Prerequisite: Pact of the Chain feature
You can communicate telepathically with your familiar and perceive through your familiar’s senses as long as you are on the same plane of existence. Additionally, while perceiving through your familiar’s senses, you can also speak through your familiar in your own voice, even if your familiar is normally incapable of speech.
Voice of the Chain Master uses the warlock's voice to communicate, but this character is mute and does not have a "voice" in the general sense.
Could this character speak through it's familiar, even if he cannot speak himself?