Ok , lets say I have a "the Greatswords" with 3 damage ON it(it has 4 HP). So my opponent attacks with a unit that has "Horrific Mutation" ( units get -1 HP when this unit attacks or defends) on it. Does my Greatswords died the moment the unit is declared an attacker or can I defend with it and it dies on step 5 (apply damage)?

According to the rules on Card Anatomy, the definition of Hit Points

7. Hit Points: The amount of damage a unit can
take. If a unit has as many damage tokens as it has
hit points, that unit is destroyed and is placed in its
owner’s discard pile.

So yes Greatswords are dead.

As I wrote on BGG with the same quote, they are dead mens. :)

I've been mulling it over for abit and I can see how it really wouldnt make sense any other way. How useful would cards like "Flames of  Tzeentch" and the counterstike keyword if units almost never die other than at the end of the turn.  Thanks for the input people...its the only way Ill learn.

...dumb chaos, Horrific Mutation only costs 2! :P

just to note. Greatswords would not die the moment that the attacker was declared but the moment that Greatswords was declared as a defender (which is optional and a way of avoiding the death).

Rules text:

The defending player now decides which of his units
in the attacked zone (if any) are going to participate
in the battle to defend the zone.