Masechet Zevachim, Perek (chapter) Gimel (three), Mishnah Aleph (one). At the beginning of the last Perek, it was mentioned that there are certain people who are disqualified from doing the Avodah (service) of the Korban (offering). But when we said that those people were disqualified from doing the Avodah, we were talking only about all the parts of the service following the Shechita (slaughter), beginning with the Kabbalat haDam (receiving the blood), then the Holacha (carrying), and then the Zrika (sprinkling). But when it comes to slaughtering the Korban, the Halacha (Jewish law) is different.
The Mishnah says that if any of the disqualified people mentioned in Mishnah Aleph in the last Perek slaughtered the Korban, the slaughter is valid, and you can continue with the rest of the Avodah. Slaughtering is valid even when done by non-Kohanim (non-priests), women, Kena'ani (Canaanite) slaves who are eventually freed, or people who are Tameh (impure). Even though these people are not allowed to do the other components of the Avodah, they are allowed to slaughter the Korban.
Because when the Torah teaches us that the Kohanim (priests) have to have a role in the Avodah, it says: The animal, the bull, was slaughtered before Hashem, and then B'nei Aharon were the ones who brought it near, and then B'nei Aharon were the ones who brought it nearer to the Mizbe'ach (altar). So you see that from the Holacha onward, it has to be B'nei Aharon. We see from this that the Shechita, which comes before the Kabbalah (blood reception), can be done even by non-Kohanim. Therefore, we can learn from this case that all other people who were disqualified from doing the Avodah are allowed to slaughter the Korban. Even when talking about Korbanot from the high category of Kodshei Kodashim (most holy offerings), a disqualified person would be allowed to slaughter this type of Korban, and if they did, it would be valid.
One qualification: we mentioned that a Tameh person is allowed to slaughter the Korban. Of course, a Tameh person is not allowed to stand in the Beit HaMikdash, so that person has to stand outside the Beit HaMikdash with a longer knife. Also, these people who were impure would not be allowed to touch the meat of the Korban after it was slaughtered, because if they touched it, they would make it Tameh, and then it would become unusable.
So what we’re concluding is that a disqualified person is allowed to slaughter a Korban. Therefore, since he is allowed to, his intentions actually could invalidate a Korban, and they make a difference. If he were not allowed to, then his intentions would be meaningless. Therefore, a disqualified person who has wrong intentions could invalidate the Korban by slaughtering it with improper thoughts. But since a disqualified person is not eligible to do the other parts of the Avodah, the Halacha is different if he does have improper thoughts. If a disqualified person receives the blood with intentions of eating the meat or burning the Emurim (sacrificial portions) past the proper time or not in the proper place, those intentions would not invalidate the Korban. Since they are not allowed to do those parts of the Avodah anyway, how could they ever invalidate it? So they would not invalidate it.
So what comes out of that: if there’s still some life left in the animal, that means there’s still some blood coming out of the neck, and a qualified Kohen, who is the only person allowed to do that part of the Avodah, should go receive some of the blood and finish offering the Korban with it. The Avodah of the disqualified person wasn’t valid. Therefore, if you have someone else who could make the Avodah valid, and there’s still blood coming out of the neck of the animal, a valid Kohen could take that blood and continue the service with it. He catches it, walks it to the Mizbe'ach, and then throws it onto the Mizbe'ach.