I suppose it depends on the context of the sentence but I would understand this to mean "don't thrown stones at me" i.e. "dont punish me"
This would come from the ancient (and very unpleasant) method of punishment by throwing rocks at them (usually until they died from their injuries) In asking someone "dont stone me" you are asking them not to punish or harrass you
If my understanding of the sentence is correct that is!
That probably refers to the punishment that was given to people who broke certain laws of their respective culture or "land". For instance, why back in the days of the bible, women who comitted adultery were literally stoned to death. Everyone formed a circle around the poor woman and picked up a bunch of stones and threw them at her until she was dead. Stoning was used for other offenses, but that is what the phrase means. It's a brutal form of punishment that I think is still practiced in some parts of the world. So when you say "don't stone me" you are really saying "don't rip me a new butthole, OK" or something to that effect. In other words, don't do something really unpleasant to me just because I did this or said that.
It means don't blame me! 'Don't stone me' is used in the context of something that has got out of control, and someone is used as a scapegoat. Think it may have something to do with being stoned from the Old Days (in the Bible) !
The context is: 1guy:How does Alyssa have find time apart from her royal duties to be a high fashion model for a national jeweler? She's a real gem. 2nd guy:Your email cut me deep,but you did not color your opinion.I was very clear. 3rd guy:You mean: the clarity was there. 2nd guy again:I was brilliant! DON'T STONE ME.