You are not going to like this answer, but your iPad Mini has gone into recovery mode.
At this point any important data that you had on this iPad, unless you had done a back up to iCloud, at some point, is already gone.
You will need to seek out a friend or family member that uses Apple iDevices and the recent iTunes on a computer to restore your iPad Mini over iTunes.
Take your iPad Mini to your “local” Apple Store to do the restore of your iPad Mini in the store.
Call the Apple Store first to make sure they can do this and, also, to make an appointment to have them do the restore of your iPad Mini.
Good Luck to You!