I'm aiming to cut shapes out of jpeg files in Illustrator, I figured the easiest way to do this was to use clipping masks.
Now, is there any way to discard everything outside of the mask, rather than hiding it? (Uploaded image incase I've been unclear)
You can't discard it because its a 'mask' (clues in the name really. lol). You could always try drawing a circle over the bit of the image you want and then with the new circle selected: OBJECT>PATH>DIVIDE OBJECTS BELOW then deleting the outer shape but I'm not 100% sure if that works with jpg's or just other vector images?
Really your best bet is going to be photoshop.... Or, if the image is ending up in an indesign document, you can either place the image into the correctly sized shape or alternatively play with the detect edges feature.