There are eight species of sour pinatas in the game. They start to intrude your garden after reaching a properly high experience level. Every visit of an animal like this is annoying and bad for your habitants.
First of all, eliminate poison sweets which they are throwing, because they make your pinatas sick. Then deal with the uninvited guest itself. Your shovel is an efficient weapon. Breaking sour pinata is nevertheless only a temporary solution.
To get rid of it once and for all, you must have in your Tower of Sour a segment representing it. You can get it in two ways: by taming specific sour pinata or by buying a totem blocks from Costolot's General Store.
We propose to use the second method first. Remember, that you can buy it after breaking up at least one sour pinata of this kind. Then check if the totem is activated. This way you keep away specific sour pinatas from your garden.
When you want to tame the sour pinata, deactivate its totem and wait until it shows up. Meanwhile prepare to fill all its resident requirements. When the animal comes in, make sure it gets whatever it needs. After it forms a cocoon, it is already ours. Now you can activate the totem again.
A tamed pinata is just like any other else. You need to fill its romance requirements, ask Gretchen Fetchem to hunt a mate for it, meanwhile build house etc. Tamed pinatas repay us in a various ways. Detailed description can be found in the chapter Pinata species.