If a deaf–mute is capable of instructing witness by writing to divorce his wife we write the Get and give it to his wife. (1)
If someone becomes mute and we ask him if he wants to write a Get for his wife and he nods his head in consent we test him and if he is mentally competent we give the Get.
A Cheresh is a person who can talk but can't hear and an Ileim is a person who can hear but can't talk.
A Cheresh who can talk and an Ileim who can hear are regarded as regular adults for everything.
A mute who swears that he isn't aware of testimony is Patur from a Korban Shevu'ah even if in truth he is aware of the testimony.(2)
A person must testify orally and not by writing down the testimony and giving it to the Beis Din. (3)
A mute may testify that a husband died in order to allow the wife to remarry.
According to the Tana Kama a deaf-mute may not divorce his wife even if he is capable of communicating by writing. (4)
R. Shimon Ben Gamliel says that someone who was originally healthy and became a deaf-mute after his marriage may divorce his wife if he is capable of communicating by writing.
A person who married when he was a deaf-mute may divorce his wife because his marriage is mid'Rabanan by means of Remizah, so therefore he may divorce with Remizah.
A deaf-mute who did Yibum with the wife of his brother who was healthy may not divorce the Yevamah according to the Tana Kama. (5)
If two brothers who are deaf-mute marry two sisters and one of them dies without children no Chalitzah is necessary.
If the two brothers who are deaf-mute are married to two unrelated wives and one of them dies without children the surviving brother may do Yibum and he may subsequently divorce her.
If the two brothers marry two sisters who are deaf-mute and one of them dies without children no Chalitzah is necessary.
If the two brothers marry two unrelated women and one of them dies without children the surviving brother may do Yibum and he may subsequently divorce her.
If a wife becomes insane her husband may not divorce her. (6)
If the husband becomes a deaf-mute or insane he may never divorce his wife. (7)
If the husband instructs witnesses to write a Get for his wife they may not give the Get unless he instructs them to give it.
R. Meir holds that Mili may be passed on from one Shali'ach to another while R. Yosi argues.
R. Meir holds that if a husband instructs three people to give a Get they may appoint a scribe to write the Get and two witnesses to sign the Get.
A BIT MORE
1. This is only true with regards to a person who was born and alter became a deaf–mute. Even if he was healthy at the time that he got married and thus his Kidushin was d'Oraisa Get may be given if he instructs the witnesses by writing.
2. Because he is Pasul for Eidus.
3. Although Edim may testify by signing on a Shtar that is because testimony in a Shtar is a usual method for testifying.
4. However if at the time he married he was a deaf–mute he may divorce his wife because just like he married b'Remizah (indicating) so too he may divorce b'Remizah.
5. If he is a deaf-mute from birth he may not divorce his wife according to everyone. If he was originally healthy and he later became a deaf-mute if he is capable of communicating by writing he may divorce her according to R. Shimon Ben Gamliel.
6. Even though a woman does not need Da'as to receive a Get however the Rabanan were concerned that once she is divorced people will act with her a Minhag Hefker.
7. This is in accordance with the Rabanan who hold that a person who becomes a deaf-mute may not divorce his wife even if he is capable of writing down that he wants to divorce his wife.
The Gemara states that a mute may testify that a husband died in order to allow the wife to remarry. However the Yerushalmi states that if a note is found which states that a man died we do not rely on it to allow the wife to remarry. The Ran explains that we only rely on writing to allow the woman to remarry if the witness intended to testify when they wrote that the husband dies. But a note that was not meant to be testimony may not be relied on.
THE GET OF A DEAF-MUTE
If a person was healthy when he married and he later became deaf-mute and certainly if he became insane he may not divorce his wife until he becomes healthy. We do not rely on indications from the deaf-mute or on his writing even though his mind is lucid. However if he married while he was a deaf-mute he may divorce his wife by indicating that he wants the Get to be written and given because just as he married by means of indicating so too he may divorce by means of indicating. (Rambam Hilchos Gerushin 2:17)