Hi Patricia,
Any drawer including the cutting board, the glides separate by holding down on one side, up on the other side, the black plastic levers on the exposed side of the glides. When holding them up/down, pull hard on the board and it will come out with resistance. If it doesn't work, flip the up/down and try again. Then you can easily remove the glides from the cabinet and board. To remove the glide from the cabinet, you have to slide the ball bearing section around to expose the screws.
Not intending to promote my sales, but are you thinking of a drawer like
THIS? Someone here, maybe it was Barry-Sue, came up with the idea. It is a quick remedy for extra storage, but a custom made drawer for that position could be made bigger yet.
If your Mr. is up to a challenge, he could attempt what I did in the end which nearly doubled our galley cabinet storage drawer space
HERE. Some was gained in the obvious places such as eliminating the center style, drawer walls, and glides, but most was gained in the depth to the back wall.