This is something of a timing question - Is the taking of damage that would destroy a card a distinct step from actually destroying a card? I've never really tried to differentiate these two, but I've come across a situation where it matters. Captain Cosmic's Dynamic Siphon grants use of a power "whenever this card is dealt damage." It has 2 HP and takes 2 HP of damage, does the use a power ability fire? Or it is destroyed simultaneously to taking sufficient damage to reduce it's HP to 0 (or below)?
It’s destroyed, and doesn’t trigger its ability.
Cards are generally destroyed before their other effects activate, unless those effects specify "when this card is destroyed...". So, constructs that are destroyed by damage will not activate their on-taking-damage effects.
Unless Fixed Point is around, of course.
He would not get to use a power. Damage occurs first, however triggers can interrupt other triggers, which is what Destruction will do. This leads to its destruction, then since it is no longer in play, it cannot do the on damage effect.
Ah well, it was worth a shot.
I don't play it that way. The card takes the damage which triggers the ability which pauses things until that happens, then things continue and the result of the damage happens (destruction). I don't even care if you're right that that's wrong, because it feels so right.
The issue is that with consecutive triggers the newest one always resolves first, interupting any previous ones (like you kinda said). In this case, destruction interupts the ability triggered by taking damage.
But as you say, it's your game to play how you want certainly.
I think I'd prefer it the way it's ruled. If it worked even after its destruction, you wouldn't be able to pull of similar shenanigans that would actually work in your favor, like Bee Bot and End of Days. If damage/destruction continues even after the card gets destroyed in the middle of its effect, Bee Bot wouldn't be able to interrupt any harmful card effects, which it CAN do.
That's not how Spiff is playing it.
He's counting the damage as resolving before destruction. Not saying destruction can't interrupt effects.
Basically destruction can't interrupt the damage that is causing the destuction.
We already know hp goes into negatives, so we know that as hHP is reduced it goes below 0 before triggering destruction. If the triggering of destruction and the triggering of taking damage reactions are simultaneous, then you could resolve them in either order.
It does lead to interesting post-death combos like the one I had in the app where Unity was incapped by a negative HP Ambuscade, but it would only effect effects that respond to taking damage.
Actually, playing the way that Spiff does wouldn't change that many shenanigans. I think that on the hero side, the biggest effects would be Cryo Bot, Vitality Conduit and Dynamic Syphon, plus some reactive effects like combat stance that would only matter when the hero is being incapped. On the villain side, it's mostly several of the title cards which care, plus some reactive effects that would almost never matter (unless you're trying to kill Ambuscade and your only remaining hero has 1 hp).
How do you play it when you're playtesting? 
Don't forget about Absolute Zero and Isothermic Transducer. You can get the last big hit or even restore back to above 0 HP if Nullpoint is also in play.
I'm sure I was playing it that same way during playtesting too. It never occurred to me that that might not be the correct way. In future playtesting, if I use Cap Cosmic, we'll see if I can remember to do it differently. 
I'm with Spiff on this one. It makes more sense to me that a card's effect on taking damage would go off before the card gets destroyed.
It would make the TtE+WtM+Cryo Bot combo an infinite damage loop.
You are free to play it that way if you want. But just know it's not technically correct
I don't know, there is this
https://greaterthangames.com/comment/61044#comment-61044
Quoted also on the document: effects on a destroyed card are in play until the card completes its destruction
In this case it would mean that for example Vitality Conduit would take the last damage necessary to kill it, but before its destruction could be resolved all effects on it would still be in play. Including the effect that triggers because of its taking damage. If merely taking damage enough to trigger destruction was enough to cancel any effect wirtten on a card Akash'Bhuta's Mountainous Carapace would work a little differently than how we know it does, and Infinitor's Ocular Swarm ould make no sense at all.
The Bee Bot / End of Days example is in my opinion a little different because Bee Bot is a second card, interrupting End of Days' resolution with a destruction effect. But with a Construct there's no second card involved in resolution, beyond the one that already damaged it.
Incidentally that could mean that AZ could stay alive after taking that last bit of fire damage with NPCU in play: depends wether bringing his HP up to positives again canceled his damage-triggered destruction or not...
But the difference is that the cards in the thread with the Christophers' answers have text that specifies on destruction so they stick around to deal with that and all other non-destruction clause text happens to remain in play. During playtesting Vitality Conduit did have on destruction effects that were removed from the printed version so we know they are not meant to work when they are destroyed.
See the spreadsheet for more information.
It could also just mean that they aren't intended to trigger when an effect destroys them without dealing them damage