And ye shall give her unto Eleazar. A clear distinction is here made between two offerings; for the people are not permitted to kill the heifer, but this is the peculiar office of the priest. Thus the people offered vicariously by the hand of the priest; and in this way also at present, although we set Christ before God's face in order to propitiate Him, still it is necessary that Christ Himself should interpose, and exercise the office of a priest. Again, the heifer was to be taken outside the camp, as a sign that it was accursed, since it was an atonement. On which account, too, the atoning victims, whose blood was carried into the Holy of Holies, were burnt without the camp; the truth of which figure was accomplished in Christ, who therefore suffered outside the gates of the city, as the Apostle testifies. (Hebrews 13:11-12.) But, because this was a species of rejection, lest the heifer should be less accounted of, or lest the Israelites should think her polluted by the curse, God shews that her blood was sacred and of a sweet savor, by commanding that it should be sprinkled seven times upon the altar, which might not be profaned by anything unclean. The same thing is most clearly seen in Christ; for although He was made a curse for us, and is called "sin," because by bearing our accursed sins upon the cross, He was our atoning victim, yet nothing was thereby taken from His purity, so as to prevent His holiness from being the sanctification of the whole world. For He offered Himself through the Spirit, and by His own blood entered into the holy place, and His death is elsewhere called by Paul, "a sacrifice for a sweet-smelling savor." (Hebrews 9:11-12; Ephesians 5:2; Philippians 4:18).

The work would necessarily require a priest; yet as it rendered him unclean for the day Numbers 19:22, the high priest was relieved from performing it.
Without the camp - The defilement was viewed as transferred to the victim that was to be offered for its removal. Under these circumstances the victim, like the defiled persons themselves, would be removed outside the camp. The particular pollution to be remedied by this ordinance was the indirect one resulting from contact with tokens and manifestations of sin, not the direct and personal one arising from actual commission of sin. So too the sinless antitype had to bear the reproach of associating with sinners Luke 5:30; Luke 15:2. And as the red heifer was expelled from the precincts of the camp, so was the Saviour cut off in no small measure during His Life from the fellowship of the chief representatives of the theocracy, and put to death outside Jerusalem between two thieves. Compare Hebrews 13:11-12.

And ye shall give her unto Eleazar the priest, that he may bring her forth without the camp, and (b) [one] shall slay her before his face:
(b) Another priest.

And ye shall give her unto Eleazar the priest,.... The son of Aaron; the Sagan of the priests, as the Targum of Jonathan calls him, the second or deputy priest; it was not to be given to Aaron, that he might not be defiled, though but for a small time, that so he might not be hindered in his office at all; but to Eleazar, to inure him to his office, and to confirm him in it:
that he may bring her forth without the camp; without the camp of Israel; Jarchi says, without the three camps, as afterwards without Jerusalem; it used in later times to be burnt on the mount of Olives; it was brought forth as impure, and was a type of Christ, having the sins of his people on him, and who in conformity to this type suffered without the gates of Jerusalem, see Hebrews 13:11,
and one shall slay her before his face; the Targum of Jonathan says, another priest; but it was not necessary that it should be slain by a priest, any man might do it. Jarchi says, a stranger slew, and Eleazar looked on; though it was not slain by him, yet it was slain before him, that it might look like a sacrifice, though not offered on the altar; and slaying of it denotes the putting of Christ to death, which was done in the presence, and with the approbation, of the priests and elders of the people.

ye shall give her unto Eleazar the priest that he may bring her forth without the camp--He was the second or deputy high priest, and he was selected for this duty because the execution of it entailed temporary defilement, from which the acting high priest was to be preserved with the greatest care. It was led "forth without the camp," in accordance with the law regarding victims laden with the sins of the people, and thus typical of Christ (Hebrews 13:12; also Leviticus 24:14). The priest was to sprinkle the blood "seven times" before--literally, "towards" or "near" the tabernacle, a description which seems to imply either that he carried a portion of the blood in a basin to the door of the tabernacle (Leviticus 4:17), or that in the act of sprinkling he turned his face towards the sacred edifice, being disqualified through the defiling influence of this operation from approaching close to it. By this attitude he indicated that he was presenting an expiatory sacrifice, for the acceptance of which he hoped, in the grace of God, by looking to the mercy seat. Every part of it was consumed by fire except the blood used in sprinkling, and the ingredients mixed with the ashes were the same as those employed in the sprinkling of lepers (Leviticus 14:4-7). It was a water of separation--that is, of "sanctification" for the people of Israel.

Eleazar - Who was the second priest, and in some cases, the deputy of the high - priest. To him, not to Aaron, because this service made him unclean for a season, and consequently unfit for holy ministrations, whereas the high - priest was, as far as possibly he could, to be preserved from all sorts of defilement, fit for his high and holy work. Without the camp - Partly because it was reputed an unclean and accursed thing, being laden with the sins of all the people; and partly to signify that Christ should suffer without the camp, in the place where malefactors suffered.