Redsn0w is one of the most widely used jailbreaking app for the iPad Mini and its other models. This is because of its effectiveness and ease of use.
To get the needed tools, visit: Jailbreak Software

Here is a way to modify your device using this program:

1.    Install iTunes

Install iTunes from the CD that came with your mobile device. If you already have it, simply update it.

2.    Download The Software

After downloading,  extract the zipped file and put it into a folder or in your desktop for you to find it easily.

3.    Download The Firmware

Look for the IPSW firmware that corresponds to your iOS and download it as well.

4.    Connect Mobile Device To PC

Connect both ends of your USB cable to your mobile device and computer.

5.    Run The Program As Administrator

To do this, right click the executable file in the folder that you just extracted. Then select to run it as an administrator. Just select “Yes” from the confirmation message that pops out.

6.    Select Firmware Version

On the wizard that appears, click browse. From there, select the location where you stored your IPSW firmware data. Just select it. A pop up message will appear again asking you if it is an MC model, so just click “No”. Then click the “Next” option.

7.    Wait

Wait for the automated process to finish.

8.    Select Cydia

Once the process is finished, some options will appear. Just make sure that Cydia is checked. You may also consider checking the other options that you want to include in your installation. Then click next again.

9.    Enter DFU Mode

Put your device into DFU mode by pressing the Power and Home buttons altogether. Follow all the instructions that the program will display. This process is important for the tool to recognize your device. Click next once you are in that mode.

10.    Wait

The software will automatically hack into your device. Just wait again for the whole process to finish until it reboots. Finally, it is done.

You can download the software here: Jailbreak Software