Yevamos, Chapter 14, Mishnah 1. This Mishnah does not deal with the mitzvah of yibum, but with marriages whose validity is only rabbinic and with the way in which they can be dissolved.
"Cheresh shenasa pikachas u'fikeach shenasa chereshes":
The Mishnah opens with two cases:
"Cheresh shenasa pikachas" - a deaf-mute man who marries a woman of full mental capacity.
"U'fikeach shenasa chereshes" - a man of full mental capacity who marries a deaf-mute woman.
In both cases the law is the same: "Im ratzah yotzi, im ratzah yekayeim" - he is permitted to divorce her with a get after the marriage, and he is equally permitted to remain married to her.
And the reason is: "Keshem shekones birmizah, kach motzi birmizah" - just as he married her through gestures, that is, through sign language or some other form of communication that is not speech, so too he divorces her with a get through gestures. Even though the validity of such a marriage is only rabbinic, the manner of communication for entering the marriage and for leaving it is one and the same: whoever can become betrothed through gestures can also be divorced through gestures.
It is worth noting that giving a get is possible in its full sense even when the woman is a deaf-mute; it is simply that here there is no need for that, since the divorce is not on a different level than the marriage itself.
"Pikeach shenasa pikachas venischareshah":
The Mishnah continues: "Pikeach shenasa pikachas venischareshah - im ratzah yotzi, im ratzah yekayeim". Here her marriage was certainly a marriage on the level of Torah law, and the divorce too is on the level of Torah law: since the woman's consent is not required for a divorce, he may divorce her even after she has become a deaf-mute. And if he wishes, he may remain married to her.
The mention of the option of remaining married to her serves as an introduction to the next case: "Nishtateis - lo yotzi". If she became mentally incompetent, he may not divorce her; rather, he must remain married to her and support her. Even though by Torah law she has enough awareness to safeguard her get, and she is fit to receive it, the Sages said that he should not divorce her, because if she were not married, we would be concerned that people would take advantage of her, since her mind is not sound.
By contrast: "Nischareish hu o nishtateh - eino motzi olamis". If the husband, after having married her while of full mental capacity, became a deaf-mute or mentally incompetent, he can never divorce her, and he has no way of dissolving the marriage in that state.
The question of Rabbi Yochanan ben Nuri:
Rabbi Yochanan ben Nuri said: "Mipnei mah ha'ishah shenischareshah yotz'ah, veha'ish shenischareish eino motzi?" - why is it that when a woman becomes a deaf-mute her husband can give her a get, whereas when a man becomes a deaf-mute he cannot give a get?
The answer of the Sages:
They said to him: "Eino domeh ha'ish hamegaresh la'ishah hamisgareshes, sheha'ishah yotz'ah lirtzonah veshelo lirtzonah, veha'ish eino motzi ela lirtzono". One cannot compare the one who divorces to the one being divorced: the woman is divorced - at least by Torah law - whether she wishes it or not, and her consent is not needed for the divorce to take effect; whereas the get that the man gives does not take effect if it is forced upon him, but only with his consent.
True, where the law requires it, the Sages instituted that we compel him to divorce, but such compulsion is effective only because in the end he yields and says "I am willing"; without that statement the get would not be effective. The woman, by contrast, is divorced even against her will - and although in a far later period it was instituted that a woman is not divorced against her will, that is a rabbinic enactment.
This, then, is the answer of the Sages to Rabbi Yochanan ben Nuri: there is no room for a comparison. The man requires a sound mind, since he divorces only of his own will; the woman, however, whose consent is not required, can receive her get even after she has become a deaf-mute.