It's unlikely that cutting off a mole will result in enough blood loss for death. Hypovolemic shock occurs when severe blood loss reduces the heart's ability to pump blood to the body. According to the U.S. National Library of Medicine, hypovolemic shock doesn't begin until a fifth or more of the body's blood is lost.
Though death from blood loss isn't a major concern when removing a mole, seeking professional medical assistance is safer than at-home mole-removal remedies. Self-removal of a mole could lead to dangerous infection or future scarring. Moles may be cancerous, according to WebMD, which means a physician should check the mole first. Mole removal can be completed in a physician's office via procedures to freeze, burn or cut away the mole.