This is the second time today I've got to talk about everybody's favourite 9th Century English medical textbook, Bald's Leechbook.
The Leechbook (lit. doctor-book in Old English) suggests:
If the blackened body is so severely deadened that there is no feeling in it, then you should immediately cut away all of that dead and the unfeeling flesh up to the living body, so that there is none of the dead body as a remnant which did not feel either iron or fire beforehand...
After that one should treat the wound just like you do that part which has any feeling, and is not entirely dead... take bean meal or oats or barley, or such meal as you think that it will take, add vinegar and honey, boil together and apply and bind onto the sore place.
Note that such a poultice applied to the wound would have a number of antimicrobial properties, not least in the honey, and would also form a barrier to inhibit further infection.
It might, of course, be necessary to amputate a necrotic limb, in which case:
If you want to cut or amputate a limb from the body then examine which that place is, and the function of the place, because if one carelessly treats that place some quickly rot, some feel the treatment later, some sooner. If you should cut or amputate an unhealthy limb from a healthy body then you cut at the limit of the healthy body, but much more cut or amputate on the healthy and living body so that you may better and sooner heal it.
It's also important to cauterize such wounds:
When you set fire upon a person then you take pond-leek’s leaf and ground salt, cover the place, then by that the heat of the fire is sooner taken away. That is useful for the bite of a botrax or a dog, if one does it immediately, and again for three nights smear with honey so that the scab may fall off more quickly.