Is it possible to reduce your autonomic response to moments of stuttering? I mean the pounding heart, tightness in the stomach, etc. If it is possible, how does one go about doing this? By just entering into more situations that evoke the "fight or flight" response?The pounding heart, and tightness in the stomach is due to a reaction to the situation you are in. Your brain has learned to associate certain situations with fear and anxiety. So the next time your brain encounters a similar situation, it automatically triggers fear and anxiety TO HELP YOU TO BE PREPARED FOR THE DANGEROUS SITUATION. The reason your brain has learned to associate certain situation with fear is because your belief system has said that the situation is dangerous.
Two things you must do:
1) Re-visit your beliefs (Is stuttering in front of people dangerous?), and change your beliefs. At the end of the day, you need to have a belief like "It is not my fault that I am stuttering and there is no reason to be scared, embarrassed, or uncomfortable."
2) Unfortunately, changing your beliefs is not enough, because your brain has learned the association and you can only undo it by learning a new association. This means that you need to enter the situation over and over again, so that your brain realizes that it's not a dangerous situation. There are several techniques to achieve this effectively: here is a rough summary.