It is a Civil matter and not a criminal one.
You will have to prove financial harm becasue of this persons actions.
What job have you lost, what clients have you lost, what sales at your store have you lost because of the false statements someone made.
Also, if that person can show that the slander was not believed by anyone, you are out of luck.
For example, if I tweet that you have sex with unicorns it may be slander, but as no one really believes you have an actual unicorn, it is more satire than slander (actual case).