This Mishnah is the eleventh, and the last in the series of Mishnayos dealing with mixed blood. The case before us: blood, part of which belongs on the inner altar - one of those five, such as the blood of the bull - and part of which belongs on the outer altar, and the two bloods became mixed together.
The rule for the mixture, says the Mishnah: the blood is poured into the drain. They wait until sunset, when the blood becomes invalid, and then they pour it out. The reason for this: just as it is forbidden to sprinkle blood whose place is outside, on the inside, so too it is forbidden to sprinkle inner blood on the outside; and the Sages do not agree that the blood should be placed in a location that is not its proper place, even though this means that the offering becomes invalid.
The view of Rabbi Eliezer:
Rabbi Eliezer maintains his position: it is permitted to place the blood in both locations, provided that he does not intend for the blood whose place is inside, when it comes onto the outer altar, to be placed there, but rather he should think of it as if it were water. And so it is throughout the entire topic. Here the Mishnah does not mention his opinion, because it has qualifications that will be detailed later, but in general this is his principle.
A kohen who actually placed the blood:
Indeed, one may not place the blood in either of the locations, but rather must wait for sunset and pour it into the drain. However, what is the law if a kohen did not ask, and went and placed the blood mixture on both altars? The Mishnah says:
He placed it first on the outer altar and then entered and sprinkled from the mixture on the inner altar - it is valid after the fact, and the sprinkling is effective.
He entered the Heichal first and sprinkled there from the mixture, and then went out and sprinkled on the outer altar - here a possible problem arises, for a completely different reason.
The invalidation of 'blood that entered the Heichal':
This problem has no connection to everything that has been explained until now; this is a new topic. The verse says: "Vechol chatas asher yuva midamah el haheichal lechaper bakodesh" - it is not eaten but burned in the fire, meaning it was invalidated. The very bringing of the blood into the Heichal is, therefore, an invalidation in and of itself.
The dispute between Rabbi Akiva and the Sages:
Therefore, if the kohen took the blood and brought it inside before going outside - Rabbi Akiva says it is invalid: the blood that entered inside is invalidated from being sprinkled outside on the outer altar. And according to his view, this is true for a chatas offering, as well as an olah, shelamim, and every type of offering, for the verse says "Vechol chatas" - and what does the word "vechol" come to add? Every offering, each of the sacrifices. From the moment the blood enters inside - it is invalidated.
And the Sages validate it: in their opinion, the "vechol" in the verse does not come to include every type of offering, but rather every type of chatas - for there are different types of chatas offerings:
The fixed sin-offering: The standard sin-offering - a female goat, brought for an unintentional sin that carries the penalty of excision.
Unusual sin-offerings: Such as the sin-offering brought by a king, which is sometimes a male, and the sin-offerings brought on the festivals and the like.
In any of these sin-offerings, if the blood was brought inside - that blood is invalidated. However, in other types of offerings, such as a burnt-offering and peace-offerings - the blood is not invalidated.
And the wording of the Mishnah: "Sheharei Rabbi Akiva omer: Kol hadamim shenichnesu lechaper baheichal - pesulim" - For Rabbi Akiva says: All blood that was brought in to make atonement in the Sanctuary is invalidated; any blood whose proper place is on the Altar, and was brought into the Sanctuary to make atonement, is invalidated; the very act of bringing it inside invalidates it in every type of offering being discussed, as it says "and any," meaning all offerings. "Vachachamim omrim: Chatat bilvad" - And the Sages say: Only a sin-offering; the blood of a sin-offering that was brought into the Sanctuary to make atonement is indeed invalidated, but the rest, meaning other types of offerings such as a burnt-offering and peace-offerings - are not invalidated.
The view of Rabbi Eliezer - even the guilt-offering:
Rabbi Eliezer agrees with the Sages that the word "and any" speaks only of a sin-offering, and yet he adds: "Af ha'asham" - Even the guilt-offering. The guilt-offering is equated to the sin-offering, meaning: Out of the eight types of animal sacrifices, the sin-offering is the issue, but also the guilt-offering - for a different reason. "Shene'emar: Kachatat ka'asham" - As it is stated: Like the sin-offering, so is the guilt-offering; the verse in Vayikra (7:7) says: "Like the sin-offering, so is the guilt-offering, there is one law for them," they have a single set of laws. Because the verse equates the guilt-offering with the sin-offering, even the guilt-offering is invalidated according to Rabbi Eliezer if its blood was brought into the Sanctuary, into the Temple.
This aligns well with the very first Mishnah of the entire tractate: There we discussed an offering that was processed not for its own sake, and we said that only the sin-offering is invalidated, as well as the Passover-offering in its proper time - and even there Rabbi Eliezer said that the guilt-offering is also similar to the sin-offering, by virtue of this very same principle.
In any event, the halachah is decided in accordance with the view of the Sages, and therefore the word "and any" speaks only of a sin-offering. The blood of an offering that is not a sin-offering which was brought into the Sanctuary - this bringing in does not inherently invalidate it.
In summary: In the final Mishnah of the series on mixed bloods we learned that inner blood that mixed with outer blood is poured into the drain after sunset, because we do not place blood in a place that is not its proper place even at the cost of invalidating the offering, and Rabbi Eliezer rules it valid according to his view. After the fact, if he sprinkled first outside and then inside - it is valid; and if he preceded with the sprinkling in the Sanctuary, we entered the topic of 'blood that entered the Sanctuary' - which according to Rabbi Akiva invalidates all animal offerings, according to the Sages only a sin-offering, and according to Rabbi Eliezer even a guilt-offering by virtue of "Like the sin-offering, so is the guilt-offering" - and the halachah is in accordance with the Sages.