One of my narrators is mute, although not deaf, and illiterate, in a time long before ours. The effect of this on her personality largely leads her to withdraw and become much more of a listener than a talker, though.
You'd be surprised how much you can get out of a character simply by nods, head shakes, and shrugs. Obviously it can be hard to have a true conversation like this without bugging the reader with "I nod" "I shake my head" because that's most of what the character can DO.
General body language can also get a lot across, depending on how perceptive another character is and how well they know her. Also, if this is first person in her head, it might be slightly easier to orchestrate conversations, just because the reader will know what she means, and that gives you a little leeway with her communication skills.
I haven't decided yet if this is cheating (it might be this draft

), but I'm pretty sure that since she can still hear, even though she loses her voice my MC will be able to talk a little, if very laboriously. So she doesn't say anything unless she has to, because she can usually get her point across in other ways. (I dunno how to test this one out without surgically removing my vocal chords or something...yea, right.)
Good luck!
ETA: In the first draft, my MC was literate. But like Finbar said, what's the point of assigning such an obstacle if I give her such an easy way out? I wanna make things as hard as possible for her. So she is illiterate.