IPA: /ˈsɜːrkəmˌsaɪzər/
KK: /sɜrˈkʌmˌsaɪzər/
A person who performs a surgical procedure to remove the foreskin from the penis, often for religious or medical reasons.
The circumciser explained the procedure to the parents before performing it on their newborn.
Circumciser is formed from "circum-" (meaning around) and "caedere" (meaning to cut). The word refers to someone who cuts around, specifically in the context of the religious practice of circumcision.
Think of someone who 'cuts around' ('circum-') — that's why a circumciser is someone who performs circumcision.