Must a Starter Finish?

The Shulchan Aruch [תקצ"ב ד] rules that the same person who blew the shofar for the first series [before mussaf] should also blow during mussaf על סדר הברכות. This ruling is based on the Ramam and is explained based on the principle that one who started a mitzva should finish it. המתחיל במצוה אומרים לו גמור.

Why then does the Shulchan Aruch rule that on Shabbos a bris milah may not be split up where one person does the mila and the second person does priya [splitting the foreskin]. Implicit in this ruling is that during the week the milah may be started by one person and finished by another. What about the aforementioned rule המתחיל מצוה אומרים לו גמור?

[The Noviminsker Rebbe Shlita]