Conditions causing complete muteness
If mutism in a player is non-selective, than focus on communication should come in the form of visual cues and physical actions. Often additional special needs technology might be available to assist the player in communicating. Try as best as you can to familiarize yourself with that technology and its needs. Does it need wifi? Will it need a power outlet? Additional space at the table? Planning accordingly might help the player feel at ease.
Separate from that utilization of things like power or action cards, written notes, and movement of miniatures, may help in communicating needs and wants of the player and their character.
If sign language is an option, then I would encourage you to pursue learning ASL. There are many free online resources, such as https://www.handspeak.com/
If mutism in the player is selective, and it is desired that the the group environment is being used as a setting to effect verbal participation from the player, then it is advisable to communicate with the caregiver to discuss methodologies and practices. For instance, it may not be preferable to “rescue” the player by providing answers on their behalf, or creating an environment that favors non-verbal communication. This is in large part a matter of guidance and clear understanding of one's role within the realm of accessibility.