iOS 6.1 beta can be jailbroken with redsn0w 0.9.15 beta 3

  Exactly as in the case of iOS 6.0.1, redsn0w 0.9.15 beta 3 can jailbreak for 6.1 iOS beta, but we are talking about one tethered jailbreak, but only on iPhone 3GS and iPhone 4. The jailbreak procedure is the one explained in This article, follow it without deviating from it and at the end you will have a tethered jailbroken iPhone 3GS/4 that will have to be started in tethered mode.