Zevachim 3:1 - 3:2

כל הפסולין ששחטו שחיטתן כשרה – and the same law applies (regarding the list provided in Tractate Zevakhim, Chapter 2, Mishnah 1 of those who are ineligible to partake of the Temple Service) even ab initio, they may perform the slaughtering [of the sacrifice] as it is written (Leviticus 1:5): “The bull shall be slaughtered before the LORD; and Aaron’s sons, the priests shall offer the blood, [dashing the blood against all sides of the altar which is at the entrance of the Tent of Meeting],” from receiving the blood onward is the command of the priesthood, teaching regarding that the slaughtering [of the sacrifice] is appropriate for a non-Kohen and those who are ineligible, and it (i.e., the Mishnah) does not teach that they slaughtered it implying that de-facto it is fine but not ab-initio, but only because they are ritually impure, for a person who is ritually impure ab-initio cannot slaughter, as a decree lest he come in contact with the flesh/meat. But an impure person who slaughtered Holy Things and fit individuals are not found [together], other than with a long knife, as for example, when he stands outside the Temple courtyard and slaughters the animal that is within the Temple courtyard, for that is slaughtering of Holy Things (i.e., animals) in the Temple courtyard, but an impure person cannot enter into the Temple courtyard. But if he was defiled by an unclean reptile, that he doesn’t defile the knife, for he is not a primary source of ritual impurity. Or someone who is defied by contact with the dead who defiles the knife to become the primary source of ritual impurity in a similar manner, and the knife defiles the meat.

לפיכך הן פוסלים – the sacrifice through [improper] intention. Since they are appropriate for this [particular] Divine Service, their intention is [an inappropriate] intention and it invalidates.

וכולן – those that are invalidated.

שקבלו את הדם – on the condition to consume and/or to offer it up outside its appropriate time framework or outside its appropriate location.

אם יש דם הנפש – still in the animal, an appropriate/fit person should go back to the Divine Service and receive [the blood] and toss/sprinkle it, and the offering will be fit/kosher. For the intention of these do not invalidate them in the reception, because they are not fit for it. For the [inappropriate] intention does not invalidate other than someone who is appropriate/fit for Divine Service, and for the appropriate thing, and in the appropriate place to perform Divine Service, as it is written (Leviticus 7:18): “it shall not count for him who offered it,” for the verse speaks about someone who is fit for offering it.

יחזיר לכשר – and he will not find fault in what that he gave to the invalid individual.

נתנו – that which was invalid.

על גבי הכבש שלא כנגד היסוד – this is placement that is not in its [appropriate] place. Or that he placed that (i.e., the blood) which should be placed below [the red line] above It, the fit/kosher individual should return and receive it. And it is necessary to tell us about all of them, for it has a remedy in its return. For if it (i.e., the Mishnah) had only taught only the first clause I might think that these that were appropriate for the Divine Service of the community such as an impure person who is worthy ab-initio for the community, therefore, regarding the individual, there is a remedy through a return, but the left [hand] which is not appropriate for the Divine Service of the community, I might say that he does not have a remedy in returning it. But if we only taught the case of someone who used his left-hand, I might think that the person using his left [hand] has a remedy in returning it, for it has acceptance on Yom Kippur, for the High Priest takes the coal-pan in his right hand and the censer in is left hand. But an unconsecrated utensil, I might so not [at all]. But if he had mentioned only the unconsecrated utensil, because it is appropriate to sanctify it, but these other cases [mentioned in the Mishnah], I would say not, so it is necessary [to mention them all] (see the Gemara, Tracate Zevakhim 26b).