Apple seeded iOS 6.1 beta 3 to developers and those who running iOS 6.1 beta 3 on their idevice can jailbreak iOS 6.1 beta 3 using Redsn0w.
You should know that this is a tethered jailbreak and works with pre-A5 devices which includes iPhone 4, iPhone 3GS and iPod Touch 4G and their is no support for iPad Mini, iPad 4, New iPad/iPad 3, iPad 2, iPhone 5, iPhone 4S and iPod Touch 5G.
Jailbreak iOS 6.1 Beta 3
2. Download RedSn0w 0.9.15b3 for Windows and Mac OS X.
3. Connect your device to computer and open RedSn0w 0.9.15b3 which you downloaded by double-clicking.
4. Click on “Extras” button.
5. Click on “Select IPSW” button and select the iOS 6.0 firmware file by navigating.
6. On the main page of Redsn0w and click on “Jailbreak” button and enter into DFU mode.
To enter DFU Mode-
* Hold down Power (corner) button for 5 seconds.
* Without releasing the Power button, also hold down the Home (bottom center) button along with the Power button for 10 seconds.
* Without releasing the home button, stop holding down the power button for up to 15 seconds.
7. Redsn0w will began preparing data of your iOS 6 firmware.
8. Mae sure that “Install Cydia” option is checked and then click the Next button to start Jailbreaking prcedure.
9. Once your device is jailbroken it will enter reboot again.
Boot Tethered iOS 6.1 beta 3
Launch RedSn0w >> Extras >> Select IPSW >> Select iOS 6 firmware >> Just Boot button.
Your device is jailbroken on iOS 6.1 beta 3.