The logic which is given against organ donation in Islam is this: "This body you have does not belong to you , it is Allah key Amanat (It is something given to you by Allah for safe keeping - this is best translation I could come up with ). So since you are not owner of your body then you cannot decide about what happens to you after you die."
It is used against organ donation , cosmetic surgery, plucking of eyebrows etc etc.
Then there are these ahadees which are used against organ donation:
Utter and Complete Paindoo Production.
That verse is irrelevant to what you are implying: "organ donation is mutilating of a body inspired by Satan."
If I die and if my kidney's can ease someone's pain, my heart can help someone survive, and if my liver can help someone drink liquids...then I will be proud of that sacrifice. It is stupidity to assume that satan is making me do it.
And its also irrelevant to mention your hadees, since not everyone really cares about those things.