You need to say the words to cast a spell. How would a deaf or mute wizard/witch do that?
In later years at school, wizards learn how to use spells without speaking them out loud. This is often done if they want to get an advantage over their opponent by giving them less time to react, but it could also be used in this case.
Unspoken spells are harder to do than spoken ones, but if it's your only option to cast them, you'll have to learn them from the first year on. You'd probably get into performing magic slower than most of the others, but since it's easier for young children to learn something new, you would probably catch up with the others pretty quickly.