1) CLIPPING THE BLACK HAIRS OF A "PARAH ADUMAH"
QUESTION: In the Mishnah (24b), Rebbi Yosi Ben Hameshulam permits moving the hair from the neck of a Bechor in order to prepare it for Shechitah, even though shearing a Bechor in the ordinary manner is prohibited. The Gemara here says that Rebbi Yosi ben Hameshulam and Rav both maintain that it is forbidden to do an act that is a "Davar she'Eino Miskaven" (an act that is done for a certain permitted purpose, but which may result in a transgression being performed inadvertently). The also both maintain that plucking hair is not considered to be an act of shearing. Therefore, the reason why one is permitted to move the hair away from the area of Shechitah is because even if one inadvertently plucks some hair, he does not transgress the prohibition of shearing a Bechor.
The Gemara challenges the assertion that Rebbi Yosi ben Hameshulam maintains that a Davar she'Eino Miskaven is Asur from a Beraisa that discusses the laws of Parah Adumah. A Parah Adumah that has two black hairs is invalid (Rashi DH Shtei). However, if the root of each of the two hairs is red and only the head (end) of each hair is black, then one may use the Parah Adumah by clipping off the black end of the hair, according to Rebbi Yosi ben Hameshulam. RASHI (DH Gozez) explains that there is no concern for the prohibition against shearing an animal of Kodshim, because the person's intention is not to shear the animal (to gain its hair), but rather to make the Parah Adumah fit for use. The Gemara's question is that we see from this Beraisa that a Davar she'Eino Miskaven is permitted according to Rebbi Yosi ben Hameshulam.
When the Gemara asks its question on Rebbi Yosi ben Hameshulam, how can it consider the act of clipping the black hairs to be a Davar she'Eino Miskaven? The person clearly intends to cut the hair off! Even if he maintains that a Davar she'Eino Miskaven is permitted, this act is not a Davar she'Eino Miskaven! (See SEFAS EMES, MELO HA'RO'IM.)
(TOSFOS (DH Gozez) learns the question of the Gemara differently from Rashi. According to Tosfos, it is permitted to cut the black hairs, and Rebbi Yosi ben Hameshulam rules that one may cut them even if he might inadvertently cut the red hairs, which is prohibited.)
ANSWER: The MINCHAS CHINUCH (#287) cites the TESHUVOS BEIS EFRAIM who explains that even though the person has intention to clip the hairs, the Torah does not forbid such shearing, because the purpose for his action is not to shear the cow, but to prepare it for use as a Parah Adumah.
The Minchas Chinuch compares this concept to a principle in the laws of Shabbos expressed by the MAGID MISHNEH (Hilchos Shabbos 12:2) and as cited by the MAGEN AVRAHAM (OC 318:36). The SHULCHAN ARUCH (OC 318:12) states that when a vessel in which water was heated is emptied of its contents, one may pour a large quantity of cold water into the vessel in order to remove the chill from the water (as long as the water will not be heated to the temperature of "Yad Soledes Bo"). Even if pouring the cold water into the vessel will strengthen the vessel (which is forbidden because of the Melachah of Metzaref), nevertheless it is permitted. The Magid Mishneh explains that the reason why the strengthening of the vessel is not a Pesik Reishei (and Asur) is because the person had absolutely no intention for the resultant Melachah. When one does an action that results in a Melachah which the person had absolutely no intention to perform, this is not considered a Melachah.
Similarly, the Minchas Chinuch asserts, when one clips the black hairs of the Parah Adumah, this act is not considered shearing Kodshim, but rather it is considered an entirely different act of making the cow fit for use as a Parah Adumah. Therefore, it is considered a Davar she'Eino Miskaven, because there is no intention at all to shear the animal.
The Minchas Chinuch says that according to this approach, Rashi will maintain that one may let blood of a Bechor that has high blood pressure (see Mishnah later, 33b), despite the fact that doing so gives the Bechor a Mum. This is permitted even according to the opinion (33b) that it is forbidden mid'Oraisa to make a blemish even in a Bechor that already has a blemish. The reason it is permitted is because when one lets the blood, one has no intention to make a Mum in the Bechor, but rather to achieve an entirely different goal -- to heal the Bechor. (See also Insights to Zevachim 91:2.) (D. BLOOM)
2) THE WOOL OF A "BECHOR BA'AL MUM" THAT BECOMES MIXED WITH THE WOOL OF OTHER ANIMALS
QUESTION: Rebbi Asi in the name of Reish Lakish says that Akavya ben Mehalalel agrees with the Chachamim that when an expert Kohen did not permit the Bechor by examining its Mum, it is forbidden to derive benefit from the hair that falls off of the animal. Rav Sheshes questions this from a Beraisa (according to Rav Nachman's explanation), in which the Tana Kama and Rebbi Yosi argue about the wool of a Bechor Ba'al Mum that becomes mixed with the wool of other animals. The Tana Kama prohibits the entire mixture. Rebbi Yosi says that one may permit the wool by examining the Mum; if the Mum is a permanent one, then the Bechor may be slaughtered and the wool is permitted. We see from the Beraisa that the wool of a Bechor Ba'al Mum is permitted even before an expert permits the animal.
Why should all of the wool be forbidden (according to the Tana Kama, and according to Rebbi Yosi when the Mum is not a permanent one) due to the Bechor's wool that became mixed with it? The prohibited wool should be Batel!
(a) The RAMBAM (Hilchos Bechoros 3:12) writes that the wool is considered a "Davar Chashuv," an object of significance, which is not Batel in any amount.
(b) The RA'AVAD (ibid.) writes that the Rabanan prohibited the mixture as a penalty for leaving the Bechor in one's possession for so long, or for actively shearing the wool.
(c) The Ra'avad writes further that since the wool is Kodshim, one can redeem it with Pidyon, and thus it is a Davar she'Yesh Lo Matirin, which is not Batel in any amount. (See also YOSEF DA'AS.)