Unfortunately, you cannot expand the storage capacity of an iPad mini or any iOS device. You can however make use of what you have and maximize your existing storage. I outline a number of tips on maximizing storage in this article, which may prove helpful.
You can use cloud based apps like Box, Dropbox and OneDrive to store photos and videos. Just upload to the apps and delete them from your camera roll. They're really nice. Another tip is to keep your messages deleted. Also, are there songs you really don't need and can delete? Some apps will accumulate cache. Facebook is notorious for that. My cousin found his Facebook app at 1 gb in size. He deleted it, then installed it back and it was reduced to about 100 mb. So there's much you can do to make space.
If your space is mainly being taken up by apps, there's little you can do, other than clearing out the app's files/data/cache (jailbreaking makes this simple). If you're storing a lot of personal files or media onto it, an external storage device would work. Some use ad-hoc Wi-Fi for connectivity and microSD cards (or HDDs/SSDs/non-removable storage) for actually storing things.
If jailbroken, you can directly access the filesystem of an SD card when using the SD card adapter, which is fine for media and personal files, but can't be used for storing apps onto with symlinks and such.