The Rambam, in his presentation of the laws of Mila, in Perek 2 Hilchot Milah, Halacha 3, describes two distinct stages of the process of circumcision (listen to audio for precise citation). First, the Mohel cuts the foreskin that covers the membrum, and thereafter rips with his nail the thin membrane underneath the foreskin. The tearing of the membrane underneath the foreskin is referred to in the Talmud as "Peri'a." From the Rambam's presentation, it appears that he understood this term to mean "tearing," and he thus viewed Peri'a as a separate stage from the Mila itself, the removal of the foreskin. In his view, the Mohel must first cut the foreskin and then proceed to tear the membrane. The Shulchan Aruch in Y"D Siman 264:3 similarly describes Berit Mila as a two-stage process.
Several earlier sources also indicate two distinct stages in the process of Berit Mila. The Talmud Yerushalmi observes the double expression God uses in introducing the Mitzva of Mila to Avraham Avinu – "Himol Yimol" (Bereishit 17:13) – and explains the two terms as referring to the "two circumcisions," Mila and Peri'a. This strongly suggests that Mila and Peri'a constitute two separate stages. Likewise, the Midrash comments that when Benei Yisrael underwent circumcision in Egypt in preparation for the Korban Pesach, Moshe performed the Mila and Aharon performed the Peri'a. Clearly, according to the Midrash, these are two distinct actions. Elsewhere, the Midrash, commenting on the verse in Tehillim (35:10), "All my bones shall declare: God, who is like You," writes that David described to God how all parts of his body were used in the performance of the Mitzvot. The fingernails, the Midrash writes, were used to perform Peri'a. Once again, Peri'a is depicted as an independent stage of circumcision, separate and apart from the removal of the foreskin (which is obviously performed with an instrument, and not with one's fingernail).
However, Rav Hai Gaon (one of the last Geonim of Babylonia, 969-1038), in one of his reponsa (Shut HaGeonim Shaare Sedek, Helek 3, Shaar 5, Siman 6) wrote that the Mila and Peri'a are to be performed simultaneously; one should sever the foreskin and the thin membrane together in a single action. He apparently understood the word "Peri'a" to mean "exposing" or "revealing," rather than "tearing." It thus refers not to a separate act of tearing the membrane, but rather to a requirement that one reveal the membrum entirely as he removes the foreskin, which entails tearing even the thin membrane underneath the foreskin. Rabbi Yosef Molcho (Greece, 1692-1768), in his work "Shulchan Gavo'ah," (in siman 264, seif kattan 27) records that this was the practice in his community of Salonica. This is also view of Rabbi Yishmael Cohen (Italy, 18th century), in his work "Zera Emet" (Helek 3, siman 132.)
As noted, however, several Midrashim, as well as the Rambam and Shulchan Aruch, indicate that Mila and Peri'a should be performed in two distinct stages. This is also the view of the Kabbalists. Therefore, despite the fact that, as Rabbi Moshe Feinstein (Russia-New York, 1895-1986) wrote in Igrot Moshe, Y"D siman 155, one may rely on the view of Rav Hai Gaon and perform Mila and Peri'a simultaneously, some make a point of hiring a Mohel who performs them separately. This appears to be the common practice in Israel today, and Chacham Ovadia Yosef n his work Yabia Omer, Helek 7, Y"D, siman 22, advocates following this practice.
Summary: Two views exist as to whether the foreskin and the thin membrane underneath should be removed in a single act, or in two separate stages. Both practices are valid, but preferably one should find a Mohel who performs the Mila in two distinct stages.
