Does Deaths Dances mitigated damage bleed for true damage?

It converts the damage which already took mitigation into account. Otherwise it would need to account for resistances again.

it deals the already reduced Damage as true damage, so it won't be double reduced.

So if you have 100 Armor meaning 50% damage reduction and get dealt 200 Damage, you will still take 100 Damage, but 70 of that instantly and 30 over 3 seconds.

According to the item's text, the bleed is dealt as true damage. I'm pretty sure the reason that it bleeds you for true damage is because they wanted it to be a high risk, high reward item. You get upfront damage mitigation but if you can't sustain through the damage you take, you'll end up getting bursted. The damage mitigation is so high now that the item's broken unfortunately.

if it did then the item would be even more op than it is currently

Death's Dance needs nerfs if anything, not buffs.