The character is enraged and not thinking rationally enough to try any real treatment for her injuries. She had already recently received a gunshot to the face (the bullet passed through one cheek and out the other) maybe within twenty minutes before the amputations and the only intervention those wounds received were some loose bandages hastily wrapped around the face.
The amputations happened quick and with clean cuts. The character is currently face down on the ground, but would try to remain awake as long as possible and struggle to move. The character is female, mid-20s, physically fit, maybe around 5'11. The setting, if relevant, is outdoors, London, early May.
Terms I've googled are combinations of: bleeding, blood loss, bleed to death, loss of limbs, traumatic amputation, severed arteries, and hypovelemic shock.