Disclaimer: this is purposefully obtuse.
Other effects in the game which explicitly state they kill you:
Shadows, succubi, massive damage, death saving throws, beholder death ray (notably not even their disintegration ray kills you), power word kill, vampires, mind flayers, night hags, drow inquisitors.
Clearly, if they intended for disintegration to kill you, they'd have said so. Since specific overrides general, and there is no general rule that disintegrated creatures are dead, I rest my case. QED.
You can also safely check with Vicious mockery. The spell can target any creature, but only damages the target if it can hear, which "inanimate" things cannot.
On the other hand, Dissonant Whispers causes the target to hear (rather than hearing being a precondition as it is with Vicious Mockery) and with this you can kill petrified creatures, thus ensuring no spell casters return them to flesh-and-blood, without damaging the statue.
This is straight up horrible. LOL, party goes on a mission to obtain a cure for petrification to save a bunch of statues only to discover that they are all a bunch of corpses because the villain is just that big of an asshole.
Hope you brought your diamond dust!