Because Qyburn may have used dark magic (necromancy) to either keep The Mountain alive or bring him back him back from the dead!
Qyburn, however, an expelled former maester with extensive medical
knowledge gained from "repugnant" and "unnatural" experimentation on
living people, suggests that he may be able to save him. Cersei
dismisses Pycelle and gives Qyburn permission to do anything he can to
save Ser Gregor (likely out of gratitude for sealing Tyrion's fate and
her 'revenge' on him for the death of Joffrey), though Qyburn says
that his unorthodox methods may "change" him. She nervously asks if he
means the process will weaken Gregor, but Qyburn knowingly assures her
it will not.
What is Dead may NEVER Die, but RISE Harder, Stronger...
Although this doesn't explain the semantics of how this happened or why the magic would effect Ser Greggor this way, Game of Thrones/A Song of Ice and Fire presents us with a rather interesting spectrum of "living-dead" characters, characters that somehow live beyond their first life and/or beyond death. It's very thematic and is one way Martin contests what identity really is.
Fire Wights - (resurrection magic): Jon & Beric
Ice Wights - Army of the Dead/reanimation of dead bodies
Wargs - In theory they could extend their life if they jump into younger bodies of a longer-living animal or in rare cases, people...
Lady Stoneheart (book only) - Thoros resurrects Catlyn Stark post red wedding, but she returns in as a raving vengeful entity.
Greenseer - sees times beyond theirs.
Three-Eyed Raven (a series of people) - Powerful Greenseers who can visit and possibly interact with the past. (However there may be predetermism and to having this ability doesn't necessary mean things can be changed)
Faceless Men - "Jaqen" (or really, the Kindly Man) shows Arya that you may not be able to kill a Faceless Men, as he poisons himself, appears to die in from of Arya, and then reappears taking the body of The Waif, and Waif disappears from the scene. In addition impersonating/using an image/face of a dead person is another way to see 'life beyond death'.
A belief in reincarnation - Azor Ahai prophecy.
Benjin/Coldhands - Something similar to a White Walker or an Ice Wight, but whose identity is still preserved and can't be controlled by WW/TNK
Glamor (Magic) - Although the Faceless Men most likely use this kind of magic too, Melisandre is able to hide her true age (200-400 years old!) via using a magical stone necklace and assorted potions.