I think you want "Don't do that top me." but maybe some example might help.
You punched me. Don't do that to me.
You dropped her very cruelly. Don't do that to me.
It is a little more difficult to make sensible sentences with "with me", but not impossible.
If you have something that you can do with someone, then you can likely say "Don't do that with me". Probably not what you meant though. It seems it must compare "with someone" & "with me".
With other guys, you laugh a lot. You don't do that with me.
All through the language lesson with those guys, you made strange faces. Don't do that with me.