The Clay Golem’s Extraordinary Ability Cursed Wound reads:
The damage a clay golem deals doesn’t heal naturally and resists healing spells. A character attempting to cast a conjuration (healing) spell on a creature damaged by a clay golem must succeed on a DC 26 caster level check, or the spell has no effect on the injured character.
This effect only relates to the damage directly dealt by a Clay Golem and not to any other additional damage a creature takes or has taken before or thereafter from other sources. The "curse" affects only the wounds and not the creature as a whole. So it's important to track the damage dealt by a Clay Golem seperately.
If the damage is healed, the creature won’t suffer any further impairments.
It’s hard to say whether a Remove Curse spell would work here. Normally, curses are caused by magic or supernatural abilities rather than extraordinary abilities. On the other hand, a "curse" is something -at least to my knowledge- which it is not clearly defined anywhere in the rules.
As a DM, I would allow to use Remove Curse to get rid of the "not healing“-property of the damage taken – but not of the damage itself.
Add-on: I just saw that that this question also appeared in the FAQ:
When does the effect of a clay golem’s cursed wound go away? Can a character use remove curse (or a similar spell) to eliminate the effect?
The effect of the cursed wound lasts until all damage dealt to the target by the clay golem has been eliminated. (In general, any healing successfully applied to the character should eliminate the clay golem’s damage first.) Even if a cleric succeeds on a caster level check to heal an affected character, if any damage from the clay golem persists after that, he’d have to make another caster level check the next time he wanted to heal that character. If you don’t want to track damage from individual foes in this way, assume the effect lasts until all damage on the character has been healed. The name of the special ability strongly suggests that any effect that affects a curse would also affect this ability. Thus, it’s reasonable to conclude that a remove curse spell would remove the cursed wound effect.