What you're describing and what is commonly referred to as FGM are completely different. You're probably talking about the procedures that used to be done at clinics by urologists and other physicians in the last years before the war. These were done in a clean & sanitary environments by health professionals who in some cases administered anasthetics. Furthermore, the procedures themselves were considered as being radical and FGM hardliners frowned upon them.

I believe they would call it "sunnah" and equate it to a blood-letting or piercing ritual instead of a serious clitorecdemy.
They do it here in the U.S. too and sometimes call it labia minora reductions or clit corrections.