There are two different methods for taking a screenshot of the Samsung Galaxy S3 Mini.
There is no practical way to take a S3 mini screen shot. Pressing the Power Button and the Home Button at the same time. When you press the Power Button and Home Button at the same time and wait for 1 second, S3 Mini takes a screenshot and saves it to the phone.
The other method to take a screenshot with the Galaxy S3 Mini is to swipe your hand vertically over the phone’s screen as shown in the image below.
You can access the screenshots you took with the Samsung Galaxy S3 Mini from the Gallery application.