Matthew,
Presuming the black(ness) is the background, whichever kind of artwork you have you can do it easily with an Opacity Mask based on a path that covers the central parts and with both Clip and Invert Mask unticked (Transparency panel); select everything.
If the parts marked with green comprise vector artwork, you can create a (compound) path correasponding to the entire greenery and use that as a Clipping Mask; select everything to form a clipping set.
If the black(ness) is part of the artwork, probably you can also just create a path with exactly the same black colour that covers the central unblack part.
Basically, all of this is just a cover up.
If you really need to get rid of things, other ways may be needed, options depending on the excact nature of (the different parts of) the artwork.