If your clay pipe is clogged, it is because you put something in it, that was supposed to burn, but didn't. The solution is to make it burn!
Here is an option on how to resolve the problem. Get a blowtorch and heat the pipe until it glows. Then carefully dip the pipe in your glass of ice tea. You will never have a problem with the pipe again!
Or, you could put some wood in your firepit and add the clay pipe to the pile. Light up the fire. Enjoy some quality time with another pipe, or family members if you must. Tomorrow morning, shift through the ashes and retrieve the pipe. I guarantee that the tobacco has been consumed. It is possible that the pipe may have a different color, but that won't affect how it smokes.