The common perspective on this is that Gregor Clegane is still "alive", in some sense. Qyburn’s use of Gregor for his experiments (touching on magic and necromancy specifically), which appear to be quite gruesome and murderous given the individuals given over to him who are killed as part of this experiment, suggests that he has been able to keep Gregor’s body functioning. Certainly, the "champion" that Qyburn alludes to (IV: 479, 656), for whom an extremely large and heavy suit of armor has been commissioned, would seem to fit Ser Gregor. If this turns out to be the case, it will remain to be seen whether Gregor—or whatever has been made of him—is still capable of independent thought and action.
Introduced into A Dance with Dragons is the silent “Ser Robert Strong”, recommended by Qyburn and placed in the Kingsguard after Cersei urged it on Ser Kevan. This is, clearly, Ser Gregor… or what remains of him. It’s noted that he does not speak (allegedly because he has sworn a vow of silence), does not seem to eat, use the privy, or even sleep, suggesting that whatever Qyburn has done has left Gregor as something inhuman and perhaps not even truly alive, as Kevan speculates.