That I can tell, genital cutting acts by 3 primary means:
1) The trauma of the amputation itself. Being taken from the mother, strapped down by strangers, the pain, and so on. This splits the core self. Later on, when threatened, this preverbal trauma part returns to protect them again. They don't know where the emotions are coming from.

2) The imbalance caused by absence of part of one's anatomy. The glans, an internal part, is left constantly exposed. The glans is still sexually sensitive. Therefore the individual is constantly being sexually stimulated. The same parts of the brain light up with sexual or aggressive states. Odds are they learn to either numb out and dsiconnect from aggressive and sexual drives, or they transmute the sexual stimulation into aggression. This manifests as amplified dominance and submission dynamics. Dominate when you're big. Passive aggressive and submissive when you're small. Good for submitting to authority.

3) Psychosocial effects. Things like incomplete sexual satisfaction. Body memories of the surgery. Knowing it was done and having to doublethink about how weird it is that someone cut off part of the most sensitive and personal part of your body, a part you grew up being told was supposedly your "private parts". Sensation that at any time the ground can come out beneath you, and everyone will turn on you (basically what happened). And the collective knowledge that "I was cut. We were cut. I will cut, we cut." Implicit knowledge, not questioned. It's a shared sacrifice.