1) The Tiferes Yisrael (1:30) explains that the basis of the Mishnah (12a) is the line which states, "v'Ein Temurah Osah Temurah." This is the relevance of this Mishnah to Maseches Temurah.

However, since the Mishnah states this line, it also states along with it a few other Halachos which follow the same model of "Ein" -- of things which "do not" happen, in a similar way that "Ein Temurah Osah Temurah."

2) The Tiferes Yisrael proceeds to discuss why the Mishnah lists certain kinds of "Ein" and does not list other kinds of "Ein." He mentions 3 examples of "Ein" which are not actually mentioned anywhere, but potentially could have been, so the question is why did our Mishnah not mention them? The first potential "Ein" is, "The cursed Sotah water does not become Sotah water unless ashes are placed in them and the Megilah is erased." This is, in fact, a true Halachah. It is mentioned in the Rambam, Hilchos Sotah 3:10, based on the Gemara, who says that earth is placed in the water and the Megilah of the Sotah is erased into it. So since our Mishnah is citing Halachos which start with "Ein," why did the Mishnah not also invent a statement of "Ein" concerning the Sotah waters also?

3) I will not mention for the moment the other 2 potential "Ein" Halachos that never were actually stated, but I will just note that the Tiferes Yisrael writes that in fact there are countless possible "Ein" Halachos that could have been mentioned. However, the "Ein" Halachos that the Mishnah here does actually mention are of a very specific nature. They are all similar to the statement, "Ein Temurah Osah Temurah," which is the basis of our entire Mishnah as I wrote above in #1.

4) The Tiferes Yisrael explains what is special about "Ein Temurah Osah Temurah." A Temurah animal is one where Kedushah has been conveyed from a Kodshim animal onto a previously Chulin animal. One might have thought that in the same way that Kedushah was transferred onto the Chulin animal, the previously Chulin animal can transfer its acquired Kedushah onto another Chulin animal. The Chidush of "Ein Temurah Oseh Temurah" is that it does not work that way. Even though the Kedushah was only acquired and was not original, nevertheless it cannot be conveyed further.

5) This is also the Chidush in our Mishnah concerning the Parah Adumah water. One might have thought that if Parah Adumah water became mixed with other water, the Parah Adumah water would pass on its Dinim to the other water. The Chidush of our Mishnah is that it does not work that way. The only way of making Parah Adumah water is by placing ashes on the water. This water must be manufactured from the original raw stage because the Dinim of Parah Aduamh cannot be conveyed from existing water to other waters, just as the Kedushah received by a Temurah animal cannot be conveyed onto another Chulin animal.

Kol Tuv,

Dovid Bloom