Exsanguinate

The substance of the brain was not congested but, on the contrary, exsanguinated.

Source: wiktionary

At the battle of Ball's Bluff, I saw a soldier having a shot flesh-wound of the left arm, who was much weakened and exsanguinated from a venous hemorrhage that was caused by applying an improvised tourniquet above the wound (it was done by a comrade), and was readily stopped on removing the cause.

Source: wiktionary

Dr. [J. Leonard] Corning first exsanguinates the part to be anæsthetized with an Esmarch bandage. He next applies a tourniquet above the bandage and the latter is removed.

Source: wiktionary

A careful dissection, however, after exsanguinating the limb, suffices to prevent serious mischief, and even in the cases where the attending vein has been injured, necessitating its ligature or extirpation (eleven cases), no gangrene followed.

Source: wiktionary