How do i complete Blood on the Ice mission if Viola is dead?

Viola only exists to set you on the path to Hjerim if you didn't get there on your own, and to tell you to deal with the court wizard.

Viola is actually wrong about the court wizard. The wizard will identify the amulet for you after Calixto, who runs the museum of curiosities, tells you it's worthless and offers to buy it. However, you can assume Viola is correct and wrongfully imprison the wizard. This will lead to another murder, most likely Nilsine Shatter-Shield. Keep the amulet; it's a unique item with a moderately good enchantment for summoners in the early game.

Viola is unnecessary, as if you follow the trail of blood from the first murder scene, you'll reach Hjerim, and if you get the OK to investigate, you can still go through the whole place and find the amulet and pamphlets. The court steward (IIRC) will suggest talking to Calixto at the Museum of Curiosities, and honestly, if you're good with sneak and a lockpick, that's all you need to effectively solve the mystery.

Present your evidence to the court wizard, and he will predict when and where the next murder will occur. Look for the NPC that shouldn't be there that time of day and wait for him to draw his weapon, but act quickly or another murder will happen.