I am being contantly harassed at a local (Public) dog park about an a minor situation that occurred 2-3 months ago between my dog and another(No dog had been injured in theeese incidents) Yet I have a handful of people who keep slandering me and threating me when I'm either here or not there

What do you specifically mean by slander? Are they publishing this in the newspapers? To file and win a suit for slander you MUST show damages. What exactly are your damages in this matter?

So go somewhere else to walk your dog until those idiots forget the incidents.

If they are merely talking about a true event that happened, they can tell the truth all day. They can voice their opinion that they would not want their dog near yours and the such.
They can not threaten physical harm.