This was addressed in an earlier version of the script (the "braid" is referred to as a "queue")
It hurts. A lot.
Cut off from their connection to Eywa and their fellow tribes-people, the Na'vi will invariably commit suicide.
WAINFLEET cuts Tsu’tey's queue off near the base. TSU’TEY SCREAMS in
agony, his nervous system exploding on overload. Grinning, Lyle holds
up the queue -- Tsu’tey's only connection to the world-consciousness
which is his life.
... [later]
TSU’TEY: I can never ride again, or bond with my woman -- or hear the voice of Eywa. I can not lead the People. You will lead them,
Jakesully.
JAKE: No. I’m not officer material.
TSU’TEY: It is decided. Now do the duty of Olo’eyctan. Set my spirit free.
JAKE: I’m not killing you.
TSU’TEY: I am already dead.