I am looking for the source of a minhag that a shochet should not be a mohel because of an incident where the mohel/shochet recited "al hashechita" and the infant died afterwards. I recall that as an "eitza" to circumvent this problem, by giving a small pegima to the milah knife.
This custom couldn't have been popular in times of the Amoraim since it is brought (BT Chullin 9a):
ואמר רב יהודה אמר רב תלמיד חכם צריך שילמוד ג' דברים כתב שחיטה ומילה
Rab Judah said in the name of Rab: A scholar must learn three things, viz.: writing, shechitah, and circumcision.
R. Yitzchak Lampronti (d. 1756) writes in his encyclopedia, Pachad Yitzchak (entry for "מוהל"; p. 35a), that he had heard of this practice but did not know of any precedent. He quotes a responsum of a certain R. Netanel Saggri who alleged that the reason for this is because the hands of a ritual slaughter can tremble as he is accustomed to having the animal die in his hands and this reaction is dangerous when performing a circumcision. R. Lempronti rejects this reasoning and demonstrates that it is factually inaccurate. However, he records that he learned from incidents which were related to him, where a shochet performed a circumcision and accidentally pronounced the blessing ״...על השחיטה״ (instead of "על המילה") and the babe died, and as a precaution people would not have a shochet do a mohel's job.
A more kabbalistic [and pietistic-cautionary] standpoint is presented by R. Chaim Elazar Shapiro, Grand rabbi of Munkatz, in his Os Chaim VeShalom (269ff.) where he states, briefly put, that one who is a steady (permanent) shochet should not be a mohel. (He likewise interprets the aforementioned passage in Chullin as mere instruction for intermittent practice.)