If my hero has a tough status card and I am dealt damage, can I use an interrupt ability to reduce or prevent that…

No. Status cards have priority over all triggered abilities, like interrupts, so the tough status card must be discarded to prevent all of the damage before any other abilities could trigger. A hero can keep their tough status card if:

1. A constant effect reduces the damage the hero takes to zero. This is because constant effects have priority over status cards.
2. The hero makes a basic defense and their DEF reduces the damage dealt by the attacking enemy’s ATK to zero. This is because a basic defense reduces the amount of damage dealt by the attacker, rather than the amount of damage taken by the defender.