Re: Medical(ish) question
Cauterization would not be effective if the blood is pumping through the stump, so no, first would be a torniquet applied before the arm was amputated, just above the cut. Then survival of the patient becomes about preventing blood loss, a wound like that could kill in a minute or less, and preventing infection. I'm guessing that in your story there are no antibiotics, so in that case you will need to look at some natural disinfectants applied immediately to the stump - someone said honey and that has been used for centuries on more minor wounds.
Cauterization might be used later, if the blood is still seeping through the wound, seeping but not pouring, as it can seal things shut, but it is incredibly painful, and the shock to a patient likely already very weak would be terrible. It was also used on open wounds when they looked to be becoming infection, though with no antibiotics, it was probably not very effective.