Yoma Chapter 6, Mishnah 7. After the previous mishnah dealt with the process of the scapegoat, our mishnah returns to the service of the Kohen Gadol in the Beis HaMikdash. Once he has sent away the scapegoat, the Kohen Gadol turns to the bull and the goat that are burned - those offerings whose blood was sprinkled in the Holy of Holies and in the Sanctuary, and which must be taken outside Jerusalem and burned.
"Ba lo etzel par v'sa'ir hanisrafin":
"Kera'an" - he cuts the animals open.
"V'hotzi es eimureihen" - he removes the fats that are designated to be burned on the Altar. These are the only portions that are not burned outside Jerusalem, but rather on the Altar.
"Nesanan b'magis" - he places those fats in a vessel.
"V'hiktiran al gav hamizbe'ach" - he burns them on the Altar.
The Gemara's precision regarding the order of the burning:
The wording of the mishnah implies that the Kohen Gadol burns the eimurim at this very stage, and the Gemara points out that this is not the case. At this stage the Kohen Gadol is still wearing the white garments in which he served in the Holy of Holies; according to the order set out in the Torah, he removes the white garments, changes into the golden garments in which he normally serves, and offers two additional offerings - "eilo v'eil ha'am", the ram he must bring for himself and the ram brought on behalf of the people of Israel. Only afterward does he burn the eimurim of the bull and the goat that are burned.
Therefore the Gemara says that the text of the mishnah must be emended from "v'hiktiran al gav hamizbe'ach" to "l'haktiran al gav hamizbe'ach" - meaning, he placed the eimurim in the vessel in order to burn them eventually on the Altar, but the burning is not performed at this stage.
Taking the bull and the goat out to the place of burning:
Let us return to the bull and the goat that are burned themselves: "Kila'an b'maklos" - they would bind the entire carcasses onto sticks and poles (and it is not necessarily the Kohen Gadol who did this himself). "V'hotzi'an l'veis hasereifah" - they take them out to the place outside Jerusalem in order to burn them. This taking out is not done by the Kohen Gadol, but by men appointed for this task.
"Um'tam'im tamid es habegadim" - those involved in taking them out become tamei, and so do their garments. From what point do they become tamei?
Tanna Kamma: from the moment they leave the wall of the Azarah - the courtyard of the Beis HaMikdash - that is the point at which they become tamei.
Rabbi Shimon: from the moment the fire takes hold of the majority of the body of the animal being burned; only then does the tumah take effect.
It is worth noting that Rabbi Shimon also disagreed regarding the scapegoat, except that there he disagreed in a manner different from the distinction before us here.
In summary: In this mishnah we learned the continuation of the Kohen Gadol's service after the sending of the goat: cutting open the bull and the goat that are burned, removing the eimurim and placing them in a vessel - while the burning itself takes place only after he exchanges the white garments for the golden garments and offers his own ram and the ram of the people; binding the carcasses onto sticks and taking them out to the place of burning outside Jerusalem by those appointed for the task; and the dispute between the Tanna Kamma and Rabbi Shimon as to when those who take them out, and their garments, become tamei - upon leaving the wall of the Azarah, or from the moment the fire takes hold of the majority of the carcass.