The Gemoro says that the Mishna mentions the number of cases (15) to exclude two other possible cases (that might have been included if we held of them). The Gemoro says that even the Amoraim who do hold of those cases agree that they are not in the Mishna, because they could not be in the Mishna due to Tzoros Tzoroseihem.
My question is that, if so, how is the number 15 a Mi'ut? (i.e. according to us, who do not hold of these cases lehalocho). If the cases could not be in the Mishna anyway, a Mi'ut does not exclude them!
Hope my question is clear
Meir Eliezer Bergman
(a) Hagaon Rebbi Akiva Eiger asks your question (Gilyon Hashas to Gitin 5a, Kushyos Atzumos to Yevamos 3b), after citing two places where Tosfos indeed upholds the principle upon which your question is based (Tosfos Gitin 5a, Nidah 18b): If something doesn't fit into the group that the Mishah is discussing, the Minyan in the Mishnah cannot be excluding it. He leaves the question unanswered.
I would suggest the following answer to your question. There are two ways of grouping cases in a Mishnah. The first is by the type of case being discussed. The second is by the type of Halachos that apply to the case (i.e. grouping together all those for which certain Halachos apply).
In the first way of grouping, it is obvious that the Minyan cannot exclude something that does not fit the grouping. (This is the way that Tosfos applies your principle in Gitin 5a and Nidah 18b.) However, in our Mishnah, the grouping is done in the second way (the group is "all women who are Patur from Yibum, they, their Tzaros and their Tzaros Tzaros"). In this case, the Minyan can exclude a case for which some of the Halachos cannot be applied (such as Tzaras Sotah and Tzaras Aylonis, which cannot have a Tzaras Tzarah). The reason for this is because the Mishnah could be read as follows: "These are the women who are Patur from Yibum, both they and whatever Tzaros or Tzaros Tzaros they may have ." This would mean that Tzaros Tzaros that any of the women in the Mishnah can have are all exempt from Yibum. If some cannot have Tzaros Tzaros but can have Tzaros, at least the part of the Mishnah about Tzaros will be applicable. In short, not being able to have a Tzaras Tzarah does not make it inappropriate to be included in the Mishnah. Therefore, if there is a Minyan in the Mishnah, it may be excluding such cases from the Halachah mentioned in the Mishnah (i.e. they are not Poter their Tzaros).
(b) To sum this up, there are three categories of "omissions" from a Mishnah or Beraisa:
(1) A case which the Mishnah seemingly has no reason to omit.
(2) A case for which not all of the Halachos of the Mishnah are *applicable.(3) A case which does not fit into the theme, or category, of the rest of the cases in the Mishnah.
In (1), we must assume that this case is excluded from the Halachah of the Mishnah even if there is no Minyan in the Mishnah - unless we can explain "Mai Shayar d'Hai Shayar."
In (2), if there is no Minyan in the Mishnah we will not assume that this case is excluded from the Halachah of the Mishnah (even if there is no "Mai Shayar d'Hai Shayar). But if there is a Minyan in the Mishnah, we will assume that this case is excluded by the Minyan from the Halachah of the Mishnah (unless we can find something else for the Minyan to exclude - as in our Gemara; or unless we can explain "Mai Shayar d'Hai Shayar - see Tosfos Menachos 18b DH Minayan).
In (3), even if there is a Minyan in the Mishnah, it will not exclude this case - and it is not even necessary to find something else that the Minyan is excluding (see below).
I believe that the source for Tosfos' (and your) principle can be found in Bava Kama 5a. We find there that an item that is not part of the category listed in the Mishnah cannot be excluded by the Minyan in the Mishnah. Moreover, such an item obviates the necessity to find something that the Minyan is excluding. The Minyan is excluding the other category of items which is not similar to the one listed - even though the same Halachah does apply to the other category of items (see Rashi and Tosfos there).
(c) Rebbi Akiva Eiger asks a much stronger question on our Gemara in his Chidushim to Kidushin 3b. How can the Gemara suggest that Rav uses one Minyan to exclude Rav Asi's Halachah, and the other Minyan to exclude Tzaras Mema'enes or Tzaras Machzir Gerushaso. If one Minyan excludes Rav Asi's Halachah, obviously the Minyan can exclude something that cannot have a Tzaras Tzarah. If so, why shouldn't the Minyan exclude Rav's own case as well - since not having a Tzaras Tzarah is not ample reason for the Mishnah to omit it!
What we have written above answers this question as well. The Minyan excludes a case for which not all of the Halachos of the Mishnah are applicable - but only if we cannot find something else for the Minyan to exclude. Since Rav found the other cases to exclude, the Minyan will not exclude his case - which the Mishnah indeed left out simply because she cannot have a Tzaras Tzarah.