Yevamos, Chapter 14, Mishnah 6. This Mishnah too follows the same pattern as the two preceding ones.
The case:
Two brothers, one a deaf-mute and one of full capacity, who are married to two sisters: one a deaf-mute and one of full capacity.
The deaf-mute brother is married to the deaf-mute sister - and this marriage is only rabbinic.
The brother of full capacity is married to the sister of full capacity - and this marriage is valid by Torah law.
If the deaf-mute brother dies:
His deaf-mute wife falls before the brother of full capacity for yibum, and the law is straightforward: there is no obligation of yibum at all, since the yevamah is his wife's sister - and his wife is married to him by Torah law. She is therefore forbidden to him as an ervah, and the prohibition of ervah cancels the obligation of yibum.
If the brother of full capacity dies:
Here lies the difficulty. The obligation of yibum is a Torah obligation, whereas the marriage of the deaf-mute brother to the deaf-mute sister is only rabbinic. It turns out that his wife is not "his wife's sister" on the Torah level, and there is no Torah prohibition of ervah of a wife's sister that would be strong enough to remove the obligation of yibum.
What, then, must he do? He must divorce his wife, since she is the sister of the woman bound to him - the sister of the woman who became bound to him through a Torah-level marriage, and he cannot remain married to her. And just as his marriage to her is only rabbinic, so too he has the ability to divorce her with a rabbinic get.
The yevamah, however, the widow of the brother of full capacity, becomes forbidden forever and has no remedy:
Yibum is not possible - since she is his wife's sister on the rabbinic level, and she is an ervah on that rabbinic level.
Chalitzah is not possible - because the yavam is a deaf-mute.
In summary: In this Mishnah we learned that when the deaf-mute brother dies, there is no obligation of yibum at all, since the yevamah is forbidden to him as an ervah by Torah law as his wife's sister. And when the brother of full capacity dies, the rabbinic marriage of the deaf-mute brother does not cancel the Torah obligation of yibum; therefore he divorces his wife, who is the sister of the woman bound to him, while the yevamah remains forbidden forever - she can neither undergo yibum nor receive chalitzah.