Free the neck root at the button*.
This Japanese saw, designed for making a cut in the middle of a panel, is ideal for starting the cut to detach the neck from the button. The curved blade helps to avoid accidentally cutting the ribs.

Incidentally, notice how small the button is, it has been trimmed after a previous neck resetting. This is very bad practice but tends to happen when it is not cost effective to do the job properly, ie by making a new neck.  Before setting the new neck, I will build this button back up with an ebony crown so that the finished neck will have the correct dimensions for strength and looks.

*Excuse fingers