Can severe hypothyroidism cause anxiety and panic attacks as well as depression?

Sometimes: Less common to cause panic, that is more common with hyperthyroidism. Certainly hypothyroidism can contribute to all of those.

Absolutely!: Any psychiatric disorder is possible with exceedingly low thyroid function, even psychosis. The best way to tease this apart is for three physicians to collaborate: primary care physician, endocrinologist, and psychiatrist. Take care.