Cognitive explanation of why beta blockers are effective for anxiety
One possibility is related to the Two-Factor theory of emotion. The theory describes how emotion is a product of both cognitive and physiological factors. Essentially, the mind tries to determine what emotion it is feeling by analyzing the body. By antagonizing epinephrine, they kind of inhibit the sympathetic nervous system. So, when a person would otherwise feel anxiety it would be associated with the effect of epinephrine. Without that cue, they would possibly interpret their feelings differently, as feeling less anxious.

http://psycnet.apa.org/journals/rev/69/5/379/