Oxygenated blood is bright red and deoxygenated blood is dark red or brown.
If you take oxygenated blood and leave it in the air it will turn dark red, then brown, then finally a bluish green from exposure to atmospheric oxygen.
Why does it oxidize this far to get a copper oxide color to it after it has passed the phase where it is the same color as iron oxide? Why doesn't it stay at the iron oxide color?
This often happens during the last few days of my period that the bleeding is extremely light and the color of it when it first comes out is reddish brown (sort of like iron oxide) and after a few hours, it starts turning bluish green (sort of like copper oxide). However, this happens very slowly and after 24 hours of exposure to atmospheric oxygen still only a fraction of the blood is further oxidized. I don't take medications or drugs that have a lot of sulfur so I don't think it is from $\ce{H2S}$ or $\ce{SO4-}$ (which would give it a dark green color, not light bluish green) and I don't have excess copper in my blood either.
I think that it is Iron(II,III) oxide with the Iron(III) released and the autoionization of water (which happens in both the liquid and gas phase) forming Iron(II) Hydroxide which can be further oxidized to Iron(III) hydroxide which has that bluish green color along with a small amount of Copper oxide forming (Due to the fact that our bodies need some copper and like Iron there is always some copper in the bloodstream).
Answer
There are two misconception behind your question:
You assume you can directly compare the colors of different compounds and derive oxidation states e.g of a heme (porphyrin) comparing to iron-oxide. No, it is not true.
You assume this whole story has anything to do with copper. No, the blueish-green is nothing to do with copper, it is a (porphyrin) degradation product.
The color of transition metal compounds mostly can be derived from the crystal field (ligand field) around the central metal ion. In inorganic iron-oxo/hydroxo compounds have different structure and hence different field than heme compounds. In heme, the N coordination of porphyrin ring is generating a very strong planar field, and the oxygen coordinates as molecule on the top of it. Charge transfer to the ring can also be an important factor in heme derivatives. As you see it is a whole complicated mass, and not much direct connection with different inorganic salts you see in lab.
The colors you see are coming from oxo-hemoglobin (which you have in your healthy blood), and most probably several steps of enzymatic degradation of heme. The porphyrin ring is oxidized and cut open by an oxygen on the the iron. Several colorful compounds are produced, including the iron complexes themselves and biliverdin (green), bilirubin (yellow). These are the same colors you see under your skin, of you hit yourself hard and have some bleeding in your tissues. First the injured area is deep red/blue, than go to greenish, finally yellowish patch. This also happens continuously in your body, when your blood cells get old, and heme is enigmatically degraded so the whole thing can be recycled: http://www.elmhurst.edu/~chm/vchembook/634bilirubin.html
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