The combat rules don’t seem to cover situations where an attack has a special effect that triggers on doing damage (or indeed, any time after the Resolve Special Ability phase).
This case came up the last time I played. I played a Tube Strike, an attack that does 3 damage and has the special ability “If this attack deals damage, discard 1 of your opponent’s Stuff Cards from play.” My opponent had in play a Rare Card, a Stuff that says “Your opponent’s attacks receive -1 damage.” The attack succeeded and I chose to discard the Rare Card. So how much damage does it do? Does the damage happen first, meaning I do 3 - 1 = 2 damage and then the special effect discards the Rare Card? Or does the special effect happen first, meaning the Rare Card goes away and I do the full 3 damage?