John Gill Commentary Hebrews 13:11

"For the bodies of those beasts whose blood is brought into the holy place by the high priest [as an offering] for sin, are burned without the camp." — Hebrews 13:11 (ASV)

For the bodies of those beasts
Not the red heifer, (Numbers 19:1–22) nor the sin offering in general, (Leviticus 6:30) nor those for the priest and people, (Leviticus 4:11Leviticus 4:12) (Leviticus 21:6Leviticus 21:7Leviticus 21:18) but the bullock and goat, on the day of atonement, (Leviticus 16:11–18Leviticus 16:27) which were typical of Christ, in the bringing of their blood into the most holy place, by the high priest, for sin; and in the burning of them, without the camp: these beasts were slain, their blood was shed, and was brought into the most holy place, by the high priest; and was sprinkled on the mercy seat, and the horns of the altar of incense; and, by it, atonement was made for the priest, his house, and all Israel;

which was a type of the death of Christ; the shedding of his blood; the carrying of it into heaven; the sprinkling it upon the throne of grace and mercy; by which reconciliation is made for the sins of all God's people:

whose blood is brought into the sanctuary :
that is, into the holy of holies, as the Ethiopic version renders it:

by the high priest for sin ;
to make atonement for it, for his own, and for the sins of his family, and of all Israel:

are burnt without the camp ,
(Leviticus 16:27) even their skins, flesh, and dung; and the men that burnt them were unclean, though, upon being washed, were received:

which was typical of the dolorous sufferings of Christ without Jerusalem, as the next verse shows; and points out the extent of his sufferings, reaching to all parts of his body, and even to his soul; and expresses not only the pains, but the shame and reproach he endured, signified by the burning of the dung; and hints at the pardon of the wicked Jews, who were concerned in his sufferings; which was applied unto them upon their repentance.