depends on the magic system i guess but also, if it's a magic world then i am sure as hell gonna try find a way to use magic even without a voice. I'm gonna think about this with speaking as a requirement to cast magic.
Basing off the mana circle you mentioned, I'm assuming you mean we are in a fantasy world so there are magical creatures. How do these creatures use magic without a voice? Even if they are required to roar to use their powers, the world is vast, there may be a species out there that don't eg. monsters without a mouth like slime. Also what is a voice? Obviously if some creatures have low intelligence they might not have a language. Then it could be that the specific frequencies of their roars that are related to their magic spells. Can we replicate it on mute magicians who haven't damaged their vocal chords by humming specific tunes to summon mana circles?
If someone has no vocal chords, then we can start thinking about what and why exactly we need to speak to cast magic. Who's listening? If it's nature/spirits/otherworldly beings, in the end we're speaking to them in a human-created. Why shouldn't you be allowed to create your own language that doesn't require a voice-box, so that you can offer your magic to the spirits for the exact same reasons as the other magicians?
hmmmmm i guess if it's a magic chant, then it'll be difficult, especially if it's one of those chants that uses things like "language of the gods". Trying to trace back origins of spells would be more difficult especially when its authenticity is backed up by history. I think if I was in this situation my first bet would be try to memorise and record the specific sounds of the chant and see if I can replicate it anywhere on my body. My first option would be my voice box (if I had one), and just try and see what kind of grunts I can do and if it's passable for a spell. With no voice chords, hmmm maybe seeing the noises I can make when flicking my mouth, exhaling while patting my mouth, clicking, clapping, stomping? If music instruments can not help cast spells, than what constitutes as an instrument? Can I create a machine that can speak for me, implant it into my body and feed it commands to speak when I need it to? What if I put it in my staff, the center conduit for magic? On that note do rerecorded chants work? Cause if they do then I can either use someone else's chant.
oooo yes chanting in the mind. I believe that boils down to the caster's intention and whether it gets properly conveyed to the source of their magic. I think in the worlds where this is applicable they say it's easier to cast magic if said out loud so it's not a common practice. Definitely the kind of place you'd want to be cast in if you were a mute magician.
Can a mute person become a magician? Since they need to cast a spell. I think they still can cultivate the mana circle.