What is the maximum lifespan of a Witcher? They are mutated creatures who age slowly as compared to humans, so how much longer than the human lifespan do they have? I want to know: what is the maximum age that a witcher has lived, considering that none of them has died of old age?
Ill-defined, but certainly several times the lifespan of a typical human. That being said, there are zero control subjects since witchers are pretty rare, tend to die before attaining old age and their creation process isn't uniform, either in terms of which school created them and/or the year of their creation.
The things that happen to a witcher's body and mind during the mutations and the Trial of the Grasses alter him forever. His body acquires new capabilities and functions beyond the reach of ordinary individuals. Firstly, the aging process slows down considerably. This means that a witcher, if not slain, can live several times as long as a normal human. The exact maximum lifespan remains unknown, as sudden violence has been and remains the cause of every death in our profession. Not a single witcher has lived out his days and died peacefully in his own bed.
Given that different schools use different herbs, spells and elixirs to mutate their test subjects, it's more than likely that along with granting differing abilities and strengths, witchers may have dramatically differing lifespans.
It's very hard to say and I don't actually think there is a definitive canon answer, as the violent nature of their occupation means that Witchers all tend to be killed via unnatural means - and so not reaching their potential maximum lifespan, which would enable it to be documented.
The pen and peper rpg lists Geralt as a year older than Yennefer (born 1173), but that might not be the same as book or game material.
But Yennefer is about the same age area at least, as Geralt still in books and games, with their history: and for scale for them both, Wild Hunter/Witcher 3 happens 1272.
And Vessemir was said to be old already, by the time Geralt was born - the wiki cites him as "at least a few centuries old" - but that's not very specific.
Only a very rough estimates can be put on actual lengths of witchers' lives, but there is some info that can be used to estimate it. Let's start with least constraining data.
Conjunction of Spheres was about 1500 years before events of books. It let the humans came to the world, where "Continent" lies, from a different one. Humans did get to the Continent about a thousand years later, though:
Kiedy pięćset lat temu nasi przodkowie wylądowali na plażach, elfy też chowały głowy w piasek.
Which means "When five hundred years ago our ancestors landed on the beaches, elves also buried their heads in the sand."
Lets put the first constraint here, why not earlier? Because witchers were created by mages specialising in mutations, specifically Malaspina and Alzur, and humans only learned to use magic about the time when they landed on the Continent. We don't know when these mages lived, but it was later then five ages before events of books.
So how much later witchers came to be? I didn't found this citation, but wiki here says that it took about two hundred years until witchers started to ride around country. That means some witchers were created earlier, but even if Vesemir, last of old witchers, was one of them I wager he was no more then 350 years old by the end of the books. In games he died few years later. In books his death was only prophetised, but some future events are shown, and with time witchers became stuff of legends. All in all I doubt Vesemir or any other witcher lived more than three hundred years, four hundred tops.
How long they could live before dying of old age we don't know, but they did age slowly, while sorcerers could stop ageing using elixir invented by Ortolan. Even this elixir didn't prevent from dying from stroke, or heart attack.
Another thing is Vesemir already shown signs of old age and that had to go worse with time if he lived on. That's even more of a guesswork now, but I doubt any witcher would live more than half thousand years, before dying of old age.
Well, this may be even more tricky. Lets compare Vesemir, as oldest known witcher, with Geralt, much younger one. Geralt's white hair was unnatural, and that was rather evident, because he "wasn't old" - certainly not enough to have completely grey hair, while Vesemir had grey beard and
był zarazem wiekowym dziadem
which means "was also age-old geezer". While it doesn't mean he was a hundred years old, and witchers aged much more slowly then normal humans, somewhat over 100 may be considered a minimal lower bound. Still, being a father figure and teacher for young Geralt and accounting lower ageing rate "so low that normal people don't notice", I think minimum 150 years old is safer estimate.