If the card Ragnarok is attached to dies at the same time as another resonator it dealt damage to, Ragnarok will still replace that resonator's destination with the removed area.
Resonators with "when ~ is put into a graveyard" triggers will not trigger when affected by Ragnarok's second Continuous replacement effect because they will never hit the graveyard.
The damage dealt does not have to be battle damage. For example, if "Cinderella, the Ashen Maiden" has this card attached to her, she will remove from the game all resonators killed by her Activate ability, and her controller will gain life equal to their DEF.