Can {Nivmagnus Elemental}'s effect work on spells in the graveyard?
While the elemental is in the graveyard? No - it's an activated ability (cost:effect) which is only usable on the battlefield.
If you're asking if you can exile spells from the graveyard, the answer is still no - a spell is only a spell while it's on the stack. In any other zone, it is either a card or a permanent.
Actually. I think he is asking: " can it trigger instants and soceries in the graveyard"?
It says that spell won't resolve... So i think you exile it while it is triggering as a spell.
Limit guessing, please.
-Testset
Keep in mind that cards are only spells in one zone: the stack. So it can only be exiled while on the stack. Just to add a little clarification.