It's neurological 100%, the flow of blood is low between the areas in brain where the sentence is formed(wernicke's area) and where the sentence is signalled to trigger the speech muscles(bronca's area). Psychological issues like anxiety increases or decreases your extent of stutter but you don't solely stutter because of your anxiety. So try to calm down and speak calmly but don't stress out if you can't, it's not completely under your control.