This Mishnah is going to list parts of korbanot (offerings) that have to be removed from the Mizbeach (altar), even if they are completely valid, the Mishnah says. The following items, if they went up to the Mizbeach, have to come down: the meat of Kodshei Kodashim (most sacred offerings) and the meat of Kodshei Kalim (lesser sacred offerings). The basar (meat) of these animal offerings is never offered on the Mizbeach. Rather, we cook it and eat it. The Kodshei Kodashim and the Kodshei Kalim are cooked and not put onto the Mizbeach.
The remainder of the Omer offering, the Omer of the Mincha (meal offering) brought on the second day of Pesach on behalf of the Jewish people. Like other Menachot, we have the kometz and the shirayim. The kometz is the amount that the Kohen (priest) removes with his three middle fingers of his hand called kemitzah (taking a handful). The shirayim are the part that is removed and remains afterward. The kometz is burned on the Mizbeach, and the shirayim are eaten by the Kohanim. So if the shirayim go up, you bring them down.
The two loaves of bread that are brought on Shavuot with two lambs are also eaten by the Kohanim. The remainder of the Menachot are also flour offerings that are brought. We have the kometz and the shirayim, like we mentioned. The shirayim are also eaten by the Kohanim, so if they go up, we bring them down. And the ketoret, which is the mixture of different spices that are brought twice a day on the inner Mizbeach.
These items have to be removed from the Mizbeach because they have no connection to the Mizbeach whatsoever. They are supposed to be eaten by the owner or, like the ketoret, burned on the inner Mizbeach. The korban olah (burnt offering) has its blood and its meat burned on the Mizbeach, but the other parts of the animal are not taken up to the Mizbeach, and unless they are still attached to the meat, we do not bring them up to the Mizbeach.
The wool on the heads of the lambs of the olah, the hair of the beards of the goats, the bones, the sinews, the horns, and the hooves, if they are attached to the flesh of the olah, are brought up to the Mizbeach with it, because the Pasuk (verse) says, “the Kohen, he burns everything on the Mizbeach.” But that is talking about while it is attached to the animal. If it was detached from the flesh, we do not bring it up to the Mizbeach, as the Pasuk tells us, “you should make your olah offerings to the flesh which is the meat and the blood,” which implies that the other parts are not brought up to the Mizbeach.
So we have a little bit of a contradiction: on the one hand, it says “all of it,” and one Pasuk says “all of the animal”; the second part says it is only the meat and the blood. So we say, ah, the first Pasuk is talking about when everything is still attached; the second Pasuk is talking about when they are not attached anymore. We do not bring anything besides the blood and the basar. We also learn from here that if you did bring up parts of the animal that were not supposed to be brought up after they were detached, we bring them down. We do not leave them on top of the Mizbeach.