I think a certain amount of anxiety is unavoidable when talking about difficult topics, but it sounds like you're getting anxious enough around specific subjects that it's becoming impossible for you to discuss them? Or is your therapist the one who's concerned about your anxiety response more than you are?

My go-to coping mechanisms are deep breathing, saying out loud that I'm feeling anxious, letting myself adopt whatever physical positions seem to help no matter how silly they look or feel, and ultimately trying to forcibly knuckle through at all costs and get whatever I can of whatever it is out in the open, bit by bit however long it takes. But your mileage may vary, and if by anxiety you mean something that's making it utterly impossible to talk, more grounding tools may be called for.