Just before the performance of a Berit Mila, the infant’s father recites the Beracha of "Le’hachniso Bi’brito Shel Abraham Abinu." The question was posed to Rav Yosef Shalom Elyashiv (1910-2012) as to whether a father may recite this Beracha if he is not able to be present at the Berit. If somebody at the Berit calls the father when the Mohel is prepared to circumcise the child, to inform the father that the Berit is about to be performed, may the father recite the Beracha at that point?
Rav Elyashiv ruled that the father can recite this Beracha even if he is not present at the Berit, because he still fulfills the Misva of bringing his son into the covenant by having his son circumcised, and the Beracha of "Le’hachniso Bi’brito Shel Abraham Abinu" is recited over the privilege of bringing one’s child into the covenant. As long as he knows when the Berit is taking place – such as via a telephone call – he can recite the Beracha.
In addition to the Beracha of "Le’hachniso," the father also recites at the Berit another Beracha – the Beracha of "She’hehiyanu." Rav Chaim Pinchas Scheinberg (1910-2012) ruled that if the father forgot to recite "She’hehiyanu" at the Berit, he may still recite the Beracha afterward, as long as he still experiences the special joy of having his son circumcised. This case could perhaps be compared to the case of one who forgot to recite "She’hehiyanu" during Kiddush on the first night of Yom Tob, who recites the Beracha when he remembers, even during Hol Ha’mo’ed. Although one might argue that the case of Kiddush differs from the case of the Berit, in that the Misva of the Yom Tob celebration continues throughout Hol Ha’mo’ed, and for this reason "She’hehiyanu" can still be recited, the truth is that the cases are, in fact, quite similar. Even after the Berit Mila has been performed, the Misva is still fulfilled throughout the child’s life, as he is circumcised and bears the mark of the covenant. As such, even after the Berit, the father can still recite "She’hehiyanu" if he neglected to recite the Beracha at the Berit, as long as he still experiences the special joy of the Misva.
The Bet Yosef (commentary to the Tur by Maran, author of the Shulhan Aruch) addresses the question (in Yoreh De’a 265) of how it is permissible for the Mohel to recite the Beracha over the Berit Mila before performing the circumcision, given that the child is exposed in the Mohel’s presence. Generally speaking, Halacha forbids reciting a Beracha in the presence of exposed body parts that are normally covered. At a Berit, however, the Mohel recites the Beracha over the Misva of circumcision with the child’s private body parts fully exposed. Citing the Rosh (Rabbenu Asher Ben Yehiel, 1250-1327), the Bet Yosef explains that the prohibition against reciting a Beracha in the presence of exposure stems from the verse, "Ve’haya Mahanecha Kadosh Ve’lo Yera’eh Becha Ervat Davar" – "Your camp shall be holy, and nakedness shall not be seen among you" (Debarim 23:15). The concept underlying this Halacha is that a Beracha must be recited in a state of Kedusha (sanctity), which would be compromised if private body parts are exposed. A Berit Mila, however, is an inherently sacred occasion, and thus the exposure of the infant’s private body parts does not affect the possibility of reciting a Beracha at this very special moment. Others offer a different explanation, suggesting that this prohibition does not apply when such a young child is exposed.
The Shulhan Aruch writes that if the child soiled himself just before the Berit, it is proper to have the filth cleaned before performing the Berit, out of respect for the Misva. Although Berachot may be recited in the presence of excrement produced by an infant who has not yet begun eating solid food, nevertheless, it is clearly more appropriate to avoid performing a Berit in the presence of such excrement, for obvious reasons.
Summary: If a father is not present at his son’s Berit, and somebody at the Berit calls him to inform him when the Mohel is about to perform the circumcision, the father may recite at that point the Beracha of "Le’hachniso Bi’brito Shel Abraham Abinu." If a father forgot to recite "She’hehiyanu" at his son’s Berit, he may recite it afterward, as long as he still experiences the special joy of the Misva. If the infant soils himself just before the Berit, it is proper to first clean the filth before performing the circumcision.