iPad Mini 3 running iOS 8.4 in TaiG
TaiG is compatible with all devices running iOS 8.1.3, 8.2, 8.3 and 8.4. You must also remove passcode and TouchID protection before jailbreak (re-enable once complete), you must also turn off Find My iPhone. Turn airplane mode on and you must have an iTunes restored version the iOS you are running or plan to jailbreak. You can download all iOS firmwares from the downloads page.
If TaiG produces an error saying Apple Driver Not Found the you can download the 64-bit version from here
UPDATE x1: iOS 8.3 is no longer being signed.
To see a list of tweaks that are compatible with iOS 8.4 then click on the link below. Most tweaks will have screenshots demonstrated on an iPad Mini 3rd Generation however the compatibility will be shown for you.
TaiG itself does no harm to the device, however each system set-up could always affect the installation and modification of system files, TechHub takes no responsibility for bricked devices. Jailbreak your device at your own risk.