The quote above only concerns wounds that have been taken, e.g a saving throw has been failed. The only way to take a wound is to a) fail a saving throw / fail any number of saving throws available to you, or b) it's a mortal wound. The armour negates the first wound inflicted, a better word to use in this situation would be 'wound generated' - Wounds are generated (inflicted), then they are either saved (if possible) or taken. This being the case, no damage is given / calculated. If it's 1 damage it's not taken, if it's 2 damage it's not taken, if it's D6 damage, no dice is rolled to calculate damage.
The way this rule works you should not be taking a saving throw at all, the first wound of any kind which has been generated against you, is ignored - no save needed. This part of the wording isn't exactly clear, but if you read the rules literally, as intended, the only way the situation can unfold is the way I outlined above. Wounds do not have damage values, weapons do.
Here's an example to make it clearer:
You take a 1 wound from a weapon that does 5 damage.
You make your saving throw.
You then take 0 damage because you passed your saving throw, you don't then take 4 damage instead.