Extra space around shape when extracting a png

I have a photos, which I want to have in round shapes like the example presented below. Anyways, when making the clipping mask in Illustrator CS6, the extra space of the image around the circle stays. So, when I extract a png file, this is what I have-the circle with transparent background, but extra space around it. I tried to just crop the file, but I have lots of them, so this would take a lot of time. I wonder if there is a way to get rid of the space inside Illustrator. e