Mirroring or reflecting back what you see is sometime that I have been taught at school but I doubt that being sarcastic would fit that. I was taught mirroring more as reflecting the emotion back. When you are sad and I want to relate to that, I might reflect part of the emotion back.
As for disliking her, I can relate. My first T had an annoying habit of getting blunt. This irritated me and fascinated me. My newer T had me worried that she didn't have the guts to get blunt with me. But, she has that ability. She is just gentler at it. So, I end up trying to figure out her thinking. I was glad when I saw that she had that ability because I need to get banged upside the head sometimes because of my extreme tendency for all-or-none thinking and other distorted thinking.
I would try to figure out if you T is trying to challenge your thinking or just being sarcastic with you. Challenging thinking can be done in a gentle way.