I don't know if it's safe to carry the mindset of 'you have to operate at a deficit to lose weight.' I think that with the right balance of nutrients and cutting out excessive calories like those from sugars and pairing that with exercise, you'd be better off.

I can't say for sure, either, but I imagine putting your body in a stressful state like depravity of nutrients could certainly induce anxious feelings. I'd guess it depends on the diet and your personal relationship with anxiety