Wizkids Rules!

Does damage done to characters over the course of a player's turn carry from phase to phase? For instance, if I am using Cyclops - Optic Blast, field him and deal three damage to my opponent's 3A 4D character, and then during the attack phase I use the Reckless Melee basic action die to deal an additional damage, does the opponent's character die before damage is dealt for attackers and blockers, letting my attack through?

Also, if I was to field two cyclops - optic blast dice, I can deal three damage to a 3A 4D character, and then another 3 damage to that character to knock him out. Correct?

If so, does this work in other situations where damage would be carried from phase to phase?

As stated in the CleanUp section of the rulebook, that is when damage to all dice clears.

To be explicit, it is the ONLY time (barring a special ability) that damage clears from dice.

Your example of fielding 2 Cyclops to deal 6 damage to KO a character works, in the same way that a fielded Cyclops could deal 3 damage, and later a character could deal damage during the Attack Step to seal the KO.

-The Dice Masters Rules Team