Did you know all supermoves are actually Quicktime Events?
As an attacker you can make bonus damage when hitting hard attack button (A on the X-Box Controller) when damage is inflicted during the supermove.
As a defender you can press hard attack on every damage instance to lower the damage inflicted.
You can see your success next to the inflicted damage, there is a red icon with two swords crossed if attack damage is boosted by the attacker or a green shield when attack damage is reduced by the defender.
So don't just sit there idly getting your face smashed.