There are no statistics that I know of on rates of survival from those times, but it is safe to say, they were not great. The standard method of treating a wound, such as one left after amputation, would be to cauterize it with either boiling oil or red hot iron. That stopped the blood flow, but enlarged the traumatized area and increased susceptibility to further infection. Keep in mind that surgeons an physicians often made ointments out of animal feces and other bacteria ridden substances and had no idea about germs.

The situation changed somewhat after a French barber surgeon Pare noticed after a battle, that his paying patients who were treated with boiling oil and ointment were doing much worse than the ones he treated with just ointment because they could not pay. After that, cauterization was gradually replaced by suturing, although in the anti-sanitary conditions the rates of infection were atrocious still. Source: Journeys in Diverse Places, Pare

TL, DR: Amputee's chances of survival were not good. Medieval physicians were just as likely to make matters worse as to help.

Please note that, in AskHistorians, proper comments are expected to be in-depth, comprehensive, and informative while properly situating the answer in its historical context. They should also be backed by appropriate primary and secondary sources, whether or not explicitly mentioned in the comment (i.e. you should always be ready to provide sources if asked). In other words, answers here should be such as an historian of the subject would give--a Wikipedia link about some vaguely matching OP's scenario absolutely does not cut it.

Thank you.

I had asked this of someone else who posted but they deleted their answer before I replied: how much would the medieval doctors and surgeons have known about the techniques detailed in this post by /u/Celebreth?

The thread is kind of old by now, but it should be pointed out that to the Greeks and Romans medicine was a semi religious field. There were certain traditions that had developed despite their lack of Germ theory or Sepsis. For instance, their surgical instruments were made of metal, Bronze, or Others including steel and precious metals etc. And as semi-religious tools, they needed to be consecrated before they were used, and if they were defiled, or used they would need to be consecrated again before they could be reused either on the same patient or a different one. These pagan requirements are eventually forgotten, or left behind, and fast forward to this thread, and we see fantastic German made instruments in the middle ages, with wooden or leather handles, that cannot be boiled without ruining them. Sepsis: enter stage left.

They (Rome) also had ligatures (sutures for closing blood vessels in lieu of cauterization, the use of which was lost in the West) Now keep in mind, that Ligatures keep popping up as "rediscovered" all the way into the early early modern period (Pfeulspeundt, Paré). But the sewing and whether it's a good idea, are not the issue. Every time we rediscover the technique, it's put away again because no cure for Sepsis was at hand, and as a result the patient that was saved from dying from the amputation itself, would then succumb to infection.

Edited After thought: The Romans might have had a better chance of survival, it's true. But it would also depend on where and when the middle ages knight was wounded. A byzantine knight would have far better chances than some western knights, unless those western knights were fighting in the east, in which case, Arabic or Byzantine medicine might have been available. Additionally, the holy orders: Teutonic, Hospital, Temple had somewhat more developed medical practices, due in part to their organization, and also in part to their relatively late exposure to the Byzantines and Arabic Schools of Medicine.

This presents a small part of the marked difference in treatment and chances for survival between the wounded of the Middle Ages and the wounded of Imperial Rome.

Follow up question(even though it's a little beyond the time period): Background: I've heard of a knight who lost a hand and was able to continue using a sword with a prosthetic hand.

In general what was the state of prosthetics in this time and more specifically how did Gotz's iron hand work?

Here's what I don't understand. According to this post, battlefield medicine was highly advanced (comparatively speaking) at least as early as the Roman Era and thus that type of information would likely have been available during the Middle Ages. Why the difference in survivability between the two eras?

Nuking the thread due to no quality answers and achievement of critical mass of Gotz von Berlichingens.