Here's my reasons for why I think Surtur is not dead:
Reason 1 (might not make that much since): Surtur says he can not die until he carries out Ragnarok. Now the goal of Ragnarok is to destroy Asgard. From what Odin tells us Ragnarok is the people and there were no remaining people on Asgard (besides Hela). If this is true overall then Surtur can't die yet.
Reason 2: Surtur was merged with the Eternal Flame which means he can't die (this already proves my point). We know that individuals resurrected by the flame can still be killed again (in the case of Fenris and the Berserkers) but its merged with him which means that his immortal. We know Surtur is merged with the flame so he is basically stuck in his bigger more powerful state. This could mean trouble.
Reason 3: He swatted the Hulk like a fly, killed Hela, and survived an encounter with Odin as hinted by Thor, what more can I say.