When you are anxious you will change your breathing pattern. Worse breathing pattern leads to worse stuttering. Besides, as the situation is stressful, you might try to force through it - which again worsens your stutter because you might experience muscle tension due to speaking with force. That is also why you stutter less when you are alone or are feeling well. The desire to be mute is an offspring of the anxiety you experience. Therefore, in the stressful situation, try to control your breathing, take you time. And slow down your speech. It will make it better. This does not mean however that a raise in anxiety will once again make your stutter appear. you need to put yourself into uncomfortable speaking situations to reduce the anxiety hit. This will help your speaking capabilities. But dont rush it. Start with little, uncomfortable situations and work yourself up.