Some people do feel this way, most likely because anxiety is so high that the high amount of nervousness makes it seem as if nothing -- no activity -- is going on at all. It feels like your mind goes blank.
While slow talk is one of the first strategies mentioned, it is the "slow" part that is important. Slowing down or calming yourself down is really what this is all about. Especially for people who respond like you do. Instead of shutting down because of anxiety, see if you can relax, loosen your muscles, tell yourself to take it easy, and take a nice deep breath. This will take some practice for you to feel the effects, but the FIRST thing we must always do in treating anxiety is to learn to calm ourselves down, relax ourselves, give ourselves some time, and stay away from pressure.
The specific "slow talk" strategy comes in when you have calmed yourself down enough so that you can, by taking your time, respond to other people calmly. Instead of giving into anxiety and the mental blockage it can cause, slow down, calm down, take it easy, relax, and take your time. When you calm yourself down and give yourself some time, you will be able to think more rationally and clearly.
But first, work on the calming down and relaxing... Don't stress on the slow talk, just keep moving along so that you can see that the "slowing down" or "calming down" is just a theme in learning to overcome social anxiety. You can slow yourself down and calm yourself down. It does take practice and time, but it is well worth it. Take it easy, relax, slow everything down, and realize the situation is not a life-and-death situation. It doesn't need to be so exaggerated.