Either right before or right after the battle of the Blackwater Varys tells Tyrion that a Sorcerer castrated him and used his genitals to perform a ritual. In S03E04 Varys reveals a man in a crate to Tyrion and Tyrion assumes that it is the Sorcerer. After this we never see the Sorcerer and it is never brought up again until Kinvara speaks to Varys about it, but it is rather a one sided conversation. So what actually happens to the Sorcerer? Varys mentions in season six that he hates torturing people but are we meant to believe that he made an exception for the Sorcerer? Even if we are never given a straight answer I would be happy with any implications we could draw from the evidence given.
As you mention, in the show he appears in just one episode of season 3. Afterwards there is no mention of what happened to the man.
The complete dialogue will help build some context for our readers:
Varys: As a boy, I travelled with a troupe of actors through the Free Cities. One day in Myr, a certain man made my master an offer too tempting to refuse. I feared the man meant to use me as I'd heard some men used small boys. But what he wanted was far worse. He gave me a potion that made me powerless to move or speak, yet did nothing to dull my senses. With a hooked blade he sliced me, root and stem, chanting all the while. He burned my parts in a brazier. The flames turned blue and I heard a voice answer his call.
I still dream of that night. Not of the sorcerer, not of his blade. I dream of the voice from the flames. Was it a god? A demon? A conjuror's trick? I don't know. But the sorcerer called and a voice answered. And ever since that day, I have hated magic and all those who practice it.
But you can see why I was eager to aid in your fight against Stannis and his Red Priestess. A symbolic revenge of sorts.
Tyrion: Yes, ahem. I feel the need for actual revenge against the actual person who tried to have me killed.
Varys: Which will require a degree of influence, which ... You do not possess at the moment. But influence is largely a matter of patience, I have found.
Once I had served the sorcerer's purpose, he threw me out of his house to die.
I resolved to live to spite him. I begged. I sold what parts of my body remained to me. I became an excellent thief and soon learned that the contents of a man's letters are more valuable than the contents of his purse. Step by step, one distasteful task after another, I made my way from the slums of Myr to the small council chamber.
Influence grows like a weed. I tended mine patiently until its tendrils reached from the Red Keep all the way across to the far side of the world where I managed to wrap them around something very special. The sorcerer.
Hello, my old friend. It's been a long time
As you can see, Varys tells Tyrion that he fought Stannis and the Red Woman to have a symbolic revenge on sorcerers; however Tyrion feels the need to exact an actual revenge on the King's Guard who tried to kill him. On that Varys tells him that he needs to be patient to have that kind of influence and mentions that he has found out that influence grows with patience, implying that he himself garnered that kind of influence after being patient for decades and now he was finally on cusp of exacting his revenge.
So one thing is clear, the man's fate wasn't pleasant. He would have been killed in the end, to be sure, however I don't think Varys would have allowed him the mercy of a quick death after so patiently waiting for the day to exact his revenge for years. He must have given him a very slow, very painful death.
Also a Reddit comment that I think is helpful here:
Varys didn't just happen to conveniently have his tormentor taken there the same time a relevant discussion about it happened to come up.
I interpreted the scene as though the man had been held captive for quite awhile. The "wasn't gonna be something nice" action that Varys took was keeping the man alive in a small box for an indeterminate amount of time.
I feel like it completely went over people's heads that the "revenge" was trapping the guy and keeping him barely alive, as opposed to just killing him.
In the books, however Varys never managed to capture the Sorcerer. He mentioned that story before the Battle of Blackwater Bay, as opposed to the show where he tells that story to Tyrion after the battle.
In ACOK, Tyrion X, he tells Tyrion about the day he was cut to explain to him that he suspects that Stannis dabbles with Dark arts and therefore Varys wants him dead. It was more or less the same as the TV show and it is an awfully large passage so I'd not be including it here.
In any case, in the books, Varys hasn't done anything to the Sorcerer. At least not anything that we know of since the Eunuch is extremely secretive about his personal life and doesn't have a POV chapter.
I don't know why but I interpreted this scene as if Varys once captured the man who had cut him and the way he was taking revenge was keeping him inside that box, like, forever, feeding him only to survive or something like that. Since in S08E05
he just passed on, I was wondering what might have happened with the prisoner...