We are studying tractate Bechoros, chapter 2, Mishnah 3, which is a direct continuation of the previous Mishnah. Here we are dealing with animals that were consecrated properly, meaning that at the time of consecration they did not have a permanent blemish that would disqualify them from being a sacrifice. Once a person has consecrated his cow, goat, or sheep, the animal receives inherent sanctity - it is sanctified in its essence, and it is obligatory to bring it as a sacrifice.
However, a special verse teaches that if it subsequently develops a permanent blemish, he is permitted to redeem it. Nevertheless, even after the redemption, a remnant of sanctity remains upon the animal, and therefore all that can be done with it is to slaughter it and eat it, and with the redemption money, a replacement animal must be purchased.
For example: A cow that was consecrated for an olah sacrifice and developed a permanent blemish - the owner redeems it, and with the money he received, he buys a new cow to serve as an olah in its place. The first cow may be eaten, but not much beyond that. Detailing this "not much beyond that" is the subject of our Mishnah.
The language of the Mishnah:
"Kol shekadam hekdeshan es muman" - Any consecrated animal (a cow, goat, or sheep) that was consecrated before it developed a permanent blemish, meaning a permanent defect that disqualifies it from being a sacrifice. It turns out that the consecration began properly.
"O mum oveir lehekdeshan" - And even if at the time of consecration it already had a defect, provided it was a temporary blemish that passes on its own. Such a defect does not impede the process, and therefore an animal with a temporary blemish is permitted to be consecrated and its body becomes sanctified, and when the blemish passes on its own, it can be sacrificed.
"Ule'achar mikan nolad lahem mum kavua venifdu" - A regular consecrated animal, designated for an olah or shelamim sacrifice, and afterward it developed a permanent blemish, such as its leg being severed. From now on, it is impossible to sacrifice it, and therefore it is redeemed, and with the redemption money, a new sacrifice is purchased.
And what is the status of the animal after the redemption? Even though it has lost its sanctity and became chullin, remnants of sanctity remain in it that restrict its use, and it is not completely chullin. Such an animal is permitted to be eaten like chullin, even outside of Jerusalem and even in a state of tumah, but in practice, not much beyond that.
The restrictions listed by the Mishnah:
"Ufatur min habechorah" - Since remnants of sanctity remain in the redeemed sacrifice, a firstborn male offspring born to it does not receive the status of a bechor. The rule is that "sanctity does not take effect upon sanctity": just as remnants of sanctity remain in the mother, so too in its offspring, and therefore it is not a bechor and its restrictions and status do not apply to it. This law is learned from the verse.
"Umin hamatanos" - Here too, according to the verses, and contrary to what might be expected: when a person slaughters his disqualified sacrifice, he is not obligated to give the kohen the gifts of the foreleg, the cheeks, and the maw.
"Ve'ein yotz'in lechullin ligazeiz ulehei'aveid" - Even after the animal has become chullin through redemption, due to the remnants of sanctity that remain in it, it is forbidden to shear it and it is forbidden to work with it as a draft animal.
"Veladan vachalban asur le'achar pidyonan" - Even after the redemption, its offspring and its milk remain forbidden.
It turns out that all that remains to be done with an animal that was deconsecrated and became chullin is to slaughter it and eat it.
An animal that developed a blemish and has not yet been redeemed:
From this point onward, the Mishnah shifts the focus of the discussion, just as it did in the previous Mishnah, without explicitly stating so. Now we are dealing with a consecrated animal that has inherent sanctity and developed a permanent blemish, but it is still awaiting redemption and has not yet been redeemed.
"Veshachatan bachutz chayav" - One who slaughters it outside the Temple courtyard is liable to kareis. Even though the animal is no longer fit for a sacrifice due to its permanent blemish, as long as it has not been redeemed, its inherent sanctity remains, and it is forbidden to slaughter it outside the Temple courtyard.
"Ve'osos temurah" - Due to that inherent sanctity, one who says regarding another animal that it should take the place of the blemished animal - not by way of redemption but by way of exchange - violates the Torah prohibition of temurah (exchange), yet nevertheless, his words take effect and the sanctity spreads. The first animal remains awaiting redemption, and the new animal becomes consecrated as well, and he now has two consecrated animals in his possession.
"Umeisu yikaveiru" - An animal that was consecrated properly and subsequently became blemished, and died before it was redeemed, its carcass retains its inherent sanctity. It is not redeemed in order to use its money for something else, and it is not given as food for dogs. The only permission was redemption for the purpose of eating, and here it is impossible to eat it since it is an unslaughtered carcass, and therefore all that remains is to bury the carcass.
In summary: In this Mishnah, we learned the law of an animal that was dedicated before it received a blemish. Once it receives a permanent blemish and is redeemed, remnants of sanctity remain in it: it is eaten like chullin, but it is exempt from the laws of the firstborn and the priestly gifts, it is forbidden to shear it or work with it, and its offspring and milk are forbidden even after redemption. And as long as it has not been redeemed, its physical sanctity remains in full: one who slaughters it outside the Temple is liable, it creates a temurah, and if it dies - it must be buried.