Not necessarily. Betablockers can treat symptoms of anxiety resulting from activation of the sympathetic nervous system by blocking the action of adrenaline on adrenergic beta receptors. They may also have psychoactive effects (for example, propanolol appears to have some effect on memory consolidation [0]) but it's the inhibition of the body's "fight or flight" response that is helpful in treating performance anxiety.
[0] https://en.wikipedia.org/wiki/Propranolol#Psychological