Yes, all three iPad mini models can be jailbroken using the Pangu jailbreak tool released on October 22, 2014. This includes the original iPad mini, iPad mini with Retina display and iPad mini 3. The Pangu jailbreak works with any device running iOS 8 - iOS 8.1. You can learn how to jailbreak your iPad or iPhone using Mac OS X here or using Windows here.
The Pangu jailbreak will not work with devices running iOS 8.1.1 or later.