John Calvin Commentary Numbers 19:3

"And ye shall give her unto Eleazar the priest, and he shall bring her forth without the camp, and one shall slay her before his face:" — Numbers 19:3 (ASV)

And you shall give her to Eleazar. A clear distinction is made here between two offerings; for the people are not permitted to kill the heifer, but this is the specific office of the priest. Thus the people offered vicariously by the hand of the priest. In this same way, even now, although we present Christ before God’s face to propitiate Him, it is still necessary that Christ Himself 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. For this reason, too, the atoning victims, whose blood was carried into the Holy of Holies, were burned outside the camp. The truth of this 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 type of rejection, to prevent the heifer from being valued less, or to prevent the Israelites from thinking her polluted by the curse, God shows that her blood was sacred and of a sweet savor, by commanding that it should be sprinkled seven times upon the altar, which was not to 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).