Beth Chapman -- Slut-Calling Case DISMISSED

Beth Chapman will NOT face any punishment for calling a teenage girl a slut and a whore and other choice names .. because officials in Colorado have decided not to prosecute her.

As TMZ reported ... Chapman -- wife of Dog the Bounty Hunter -- got into a verbal smackdown with the girl back in July during a fishing trip to Monument Lake, CO.

According to police, Beth got pissed when the girl and a male friend drove dangerously close to her family while walking near the lake. She and the girl started arguing ... and Beth allegedly ripped the girl a new one by calling her all kinds of bad names.

The girl filed criminal harassment charges against Chapman ... because using "coarse language" can be considered a crime in Colorado in some situations.

But the DA apparently didn't see it that way .. because the charge has now been dismissed.