Scholarly Reflections
Daly, Robert J. "Part 2: From the Old Testament to the New. Chapter Five: Circumcision." Christian Sacrifice: The Judaeo-Christian Background Before Origen. Washington, D.C.: The Catholic University of America Press, 1978, 187-195.
In Daly's opinion, circumcision was taken over by Israel from a primitive rite in Canaan, a ceremony of which we do not know the significance (Daly 1978, 187). He speculates that it may have had some relationship to marital intercourse but was later applied to babies and possibly took on a relationship to sacrifice, though it was more commonly understood as a rite of initiation (Daly 1978, 188).
The narrative of Moses' circumcision, from Exodus 4;24-26, a challenging passage which refers to Moses as "a bridegoom of blood," is expanded upon slightly in the Septuagint and the targums, saying that the circumcision's blood is the essential element (Daly 1978, 189). This suggests that Moses' recovery is due to blood shed as a substitute for his death.
The blood of circumcision is also sometimes associated with the Passover, as the people who had not been circumcised in the wilderness received the sign just before celebrating Passover in Canaan (Daly 1978, 191). The various midrashim discuss this connection and consider the relationship to hold together through the concept of blood making atonement. Ezekiel 16:6, referring to "two bloods" is also traditionally taken to refer to the blood of circumcision (Daly 1978, 192).
Though circumcision was primarily seen as the sign of entrance into God's covenant, the idea of sacrificial blood was not absent (Daly 1978, 193). However, Daly observes that in the New Testament, Paul does away with the blood significance of circumcision and uses it rather as the cultural attribute of Judaism (Daly 1978, 194). This was a radical departure from Israelite thought.