Is it considered as of the self-defence if I hurt a dog with a cutter ?

Find another park. If there aren't any, then, you need to pick up your little dog when her dog comes around and either leave or move to a different section of the park. I do not understand why the judge said for you to take care of your behavior. Have you threatened to do anything or made any moves to do anything against this woman or her dog? This all sounds pretty petty to me in that it sounds like perhaps this woman's dog is not TRYING to actually bite your dog, but, rather just plays rough. If it wanted to really hurt your dog, I do not see why it couldn't have already done so. It sounds like her dog is just overly friendly/rambunctious/maybe obnoxious and needs some training. Perhaps you could offer some suggestions to her for controlling her dog rather than getting upset?