The Shulchan Aruch (Yoreh De'a 265:12) records the custom to conduct a special meal on the day of a circumcision (listen to audio for precise citation). The Rama (Rabbi Moshe Isserles, Cracow, Poland, 1530-1572), in his glosses to the Shulchan Aruch, adds that this meal has the status of a "Se'udat Mitzva" a meal involving a Mitzva. And one who does not participate in this meal, the Rama adds (based on the Gemara in Masechet Pesachim), is considered "excommunicated by the heavens."
The Shevet Ha'levi in Helek 8, SIman 217, (work of responsa by Rabbi Shemuel Wosner, a contemporary halachic authority in Bnei-Brak,) addresses the question of whether a Mohel, who, of course, attends many Beritot, must stay for the meal every time he performs a circumcision. Very often a Mohel must rush to perform another Brit or to examine a baby for a Brit, and it is difficult for him to stay for the meal. Is he, too, required to participate in the meal after every circumcision he performs?
The Shevet Ha'levi rules that somebody who must tend to another Mitzva is undoubtedly exempt from participating in this Se'udat Mitzva, and therefore a Mohel who has other circumcisions to tend to need not stay for the meal. Furthermore, the Shevet Ha'levi writes that a person who has a regular Shiur (Torah class) or private study session at that time is likewise exempt from participating in the meal following a Brit. This is also the ruling of Chacham Ovadia Yosef, in his work Yabia Omer, Helek 4, Siman 19. Chacham Ovadia adds that if somebody cannot stay after a Brit for the meal because he must be somewhere else, he should take some food from the meal and eat it when he arrives.
It should also be mentioned that according to some Rabbis, the Halacha mentioned by the Rama, that one faces "excommunication" if he declines an invitation to participate in the meal after a Brit, does not apply nowadays. The Aruch Ha'shulchan, ibid Seif 37, (work of Halacha by Rabbi Yechiel Michel Epstein of Navarduk, Lithuania, 1829-1908), for example, writes that the obligation to take part in a Se'udat Mitzva stems from the opportunity these events present to be in the presence and company of Torah scholars. Nowadays, however, many "improperly-behaved" people participate in these affairs, and therefore the "excommunication" does not obtain. Others claim that once a Minyan is already present at the Se'udat Mitzva, one does not bear an obligation to participate. Still others argued that invitations today are given purely for the purpose of etiquette, and do not actually impose an obligation upon a person to participate in the Se'udat Mitzva.
Therefore, although one should certainly endeavor to participate in the Se'udat Mitzva after a Brit, a person who must tend to a Mitzva or other pressing matters is allowed to leave without taking part in the meal.
