This would be a civil suit. Unless she is in violation of a order in your decree (not to "denegrate" you to 3rd parties). Either way, think about if it is worth it?
Before you get too far with this, how much money are you going to spend on attorney's and others to get diposed statements, pay to have the ex served, pay for an attorney to prepare a court case, pay for an an actual court case with attorney(s), what your time is worth, etc...Vesus what you MIGHT get in a expensive civil suit or from a female biased familly court system? Most likely, the worse that will happen to her is a slap on the wrist. How much money has her spreading untruths cost you in lost wages? How much has the mental anguish cost you in lost income? Get where I am going with this?
Unless the lies are really severe; like she said you rape small children or something to that degree, and many people have been told this , its not really going to be worth your while IMHO. Most likely, the worse that will happen to her is a slap on the wrist.
Sounds like mom is having a hard time with perhaps loosing "her" CS and has "issues" that she had been unable to change/clear up in her head since the divorce many years ago. Chalk it up to her mental issues, and be straight with the adult child if they ask about it. The adult kid can make up thier own mind. I'm sure the person who asked you/told you about what she is saying was told it's a lie by you and is spreading that out as well.
Be the MAN you have always been and rise above her petty high school behavior. The best revenge is a life well lived. Ex is probably seeing that you are well past all this and its making her wallow in her misery.
You dont owe her any money, the kid is an adult and can not be used as a weapon aainst you anymore. You are in a great place, turn on the ignore filter, and tell her you dont care what she does. She cant do anythin to you anymore. It's truely done you lucky SOB.