end of spoilers
Could Satan get killed or be to die and perish as a result of any combat or slayment? Or would such be particular and remarkable enough to leave to imagination or mystery or for following up on properly if needed - and thus initially for keeping it off panel?
I mean think about it: if Satan would die, as being the lord of darkness metaphorically, wouldn't his positive or holy counterpart like a lord up in heaven be to die also?
Maybe Hellboy thrusting his weapon onto Satan or any Satan-like entity, would primarily mean Hellboy as to be saying "No way Hose. Move along. We're not buddies, you and me."
Demons or either deathkeepers or endbringers are usually depicted as being such: they don't die. Because they'd be demons. Metaphores or neither living nor dead beings.
Read back upon Hecate - who might have died due to Hellboy putting effort into that plus for her being part human. Whereas Astoroth just goes 'Poof!' when he does. Hellboy mainly appears to be battling monsters back to where they came from, but Hellboy doesn't seem purely focused on killing them necessarily - because it might be some monsters don't get killed.
Would be my take, cautiously, since I'm still reading or getting my mitts 'round these wonderful issues.