The green part and the part with the button should come out as one piece.
There's a possibility the button release isn't working for some reason, preventing it's release. But assuming that's working . . .
Well, I'm just guessing, but I'm thinking the green part and the metal piece it's in (with the black button) are the end of an XLR cable which probably separated from the cable due to the cable's female connector seizing in position and the cable pulled loose or was manually disconnected.
You could just assemble a new cable onto what you have, or I would try a couple of other things. Squirt some WD-40 into the end of the mic through that gap, let it soak for a bit, then grab it with your hand, holding the black release button down and wiggle the hell out of it while pulling. Repeat if necessary.
A slightly more drastic method would be to soak it in WD-40, then use a large Vise-Grip pliers to clamp down on the metal part making sure the pliers compress the black button. Adjust the pliers to give a non-slip grip and use them for leverage while attempting to pull loose from the mic housing.