Exitium is a noun , and technically malum is an adjective (though it's often used substantively), so the phrase together means "evil destruction." That's not what you're going for.
You have several option for "destroy", though, so ultimately it's a matter of picking what sounds best. One option is dele malum. This means something along the lines of "put an end to evil." Scipio, in conquering the Carthaginians, futura bella delevit, "put an end to future wars" (Cic. Amic. 11).
The word has a biblical sense to it, as well. In Genesis 6, when god is talking to Noah, he says that he delebo...hominem "will destroy man." In 6.13, though, he uses the word disperdo, so that's another option. That form would be disperde malum.
Funnily enough, there's yet another word used in the passage at 6.17, interficere, though that most often is a straight forward word for "to kill." It returns to delere in 7.23.
Another very good word to use, that also has a biblical feeling to it, is perde. Classicists will know it from Catullus 8, Catullus' mourning of his lost (perditum) love with Lesbia. Those reading the Vulgate might recall a question Jesus asked the "scribes and Pharisees" about the Sabbath, "if it's permitted to do good on the sabbath or to do evil (malum), to save a life or to destroy (perdere) it?"
Personally, I prefer this one best. It really has the sense of "destroy utterly", whereas delere to me sounds too much like "delete", though clearly this is just my Anglophone ears reacting to the otherwise healthy Latin word. Still, can't beat Catullus. I also think the imperative of delere (i.e. dele) looks funny, too, especially compared to perde.
To sum up, my suggestion is: Perde Malum.
There's a lot to play around with, too, if you want to add more than a simple "destroy the bad."