You would be correct
Havengul activates ability, targeting Snapcaster Mage in non-active players graveyard
Active player declines to add anything additional to the stack, passes priority to non-active
Non-active player decides to pay delve cost (by exiling Snapcaster as part of the cost) and casts Murderous Cut in response, targeting (i'm guessing) Havengul Lich
Non-active has nothing, active has nothing, stack resolves accordingly, Murderous destroys Havengul and Havengul's ability attempts to resolve, but since Snapcaster is no longer in the graveyard it does not work.