It's a bit weird -- beta blockers are not technically, from a doctor's perspective, anti-anxiety meds. They suppress the _physical_ symptoms of anxiety, such as increased heart rate. For many people, that seems to have a big impact, and even reduce or eliminate the subjective feeling of anxiety too (specifically when used for performance anxiety; I don't know about other cases.)

I don't think we really have a good understanding of how all this stuff is connected.