If Adam would have been worthy and would not have sinned, then all of his descendants would have been worthy of the Torah. If not for Adam's sin, all mankind would have had the status of Israel. . . To some degree, circumcision restored Abraham and his descendants to the status of Adam before his sin. . . The Israelites were thus totally sanctified to God, and became virtually a separate species.
Rabbi Aryeh Kaplan, Handbook of Jewish Thought, p. 39, 47, 54.
Rabbi Kaplan's statement condenses a lot of what's been said in two recent threads. In a nutshell, so to say, circumcision is related to
parah adumah by the fact that just as
ha-adam is said to be created from the place of his atonement (
Midrash Rabbah, Bere****h XIV, 8), so that when he actually requires salvation (after the first, or original, sin), it's already there since the menstrual blood מי נדה of the
parah adumah, from whence he's created, is the means for rectifying his sin.
Similarly, the "nation" of Israel (rather than
ha-adam, or an individual Jew) is created from the place of their atonement, the blood of the lamb placed on the doorposts at the night of their creation as a nation, which, that blood, according to the chazal, was mingled with the blood of circumcision. Like
ha-adam, the "nation" of Israel is created from the place of their atonement, the blood of their atonement (lamb and limb), so that when they stumble, as
ha-adam stumbled, they too will have been created already ready to rectify their sin (the golden calf).
Ironically, according to Jewish scripture, and no less a sage than Rashi, the
parah adumah, i.e., the place of
ha-adam's atonement/salvation, is the very waters of
niddah מי נדה that cleans Israel from her first, or original sin. Ergo, there's a fundamental, symbiotic, relationship between the blood of the
parah adumah, manufactured from its sacrifice, and the blood of circumcision, which, the latter, is mingled with the blood of the Passover lamb on the night of Israel's creation as a nation, which is, ironically, the night of their salvation too.
Naturally the relationship between the blood of the
parah adumah, manufactured as the waters of
niddah מי נדה, since they're used to cleanse Israel from her original sin, the golden calf, are related to the blood of circumcision, through which the individual Jew (rather than the nation) is created, and born, and or baptized
to enter into his Jewish mission (Rabbi Hirsch). So we shant be too quick to be mixing, or combing bloods, if we were wont to note not just two blood relationships, the
parah adumah, and circumcision blood, but three,
parah adumah, circumcision blood, and the blood of the lamb; all of which are mixed or mingled (sometimes even mangled) throughout the text of the Tanakh.