From the pictures, the black part and the blue part are designed to have an adjustable sliding fit, and the silver threaded bits are nuts which form a clamp with the bolts that have been removed.
The nuts should come out with careful tapping and proper support of the other parts, and that might start to separate the alloy parts. Try tapping sideways in both directions, and try rotating them too - clockwise from the view in the picture. They can also be levered using a thick screwdriver or rod in the slot at the edge.
Proper support means solid and as close to the bit you want to shift as possible. 'Engineering is all about getting the force in the right place', as my Grandad used to say.
If you get nowhere with any of that, you need to choose between giving up and keeping your bent but working hanger, and the 'all or nothing' approach of hacksawing the old hanger into two parts at the axle dropout slot to leave two separate parts, as long as they can be for maximum leverage, which you can then work away at separately.
If it is a corrosion issue, which is likely, bear in mind the frame and new hanger might not have the best fit, depending on the level of damage.
I'm assuming the adjustment screw at the bottom is not causing any difficulty...
