I’d try lifting it out first which often works. Using a scalpel I would score around any areas of the nut which may have finish joining (edges and headstock side). Also pay special attention to scoring the edge where the repair was. Typically rosewood fender necks have the nut installed after finish, so should be reasonably safe, but you can’t be too careful! Then I would get some pincers/fret pullers on it. Grip it from above and try to wiggle it towards the headstock and back (towards fretboard). Usually there isn’t much glue holding them in place and it isn’t very resistant to flexing/movement.
If that doesn’t work you’ll need to collapse the nut as mentioned above and remove it in pieces using whatever tools you’re comfortable with…obviously don’t tap or put pressure towards either bass or treble direction or you’ll pop the binding off. Here’s one of my videos (around 2:00) where I did something similar on a neck without binding. As you have binding at the edges you won’t be able to extend the slot used to collapse the nut all the way down, but it should still be enough.
Obviously fitting the new nut is a little
more challenging too, as you’ll want it to drop in from above and fit nice and tightly.