I use a sharp knife like a craft knife or a Stanley and a pair of needle nose pliers.

Run the sharp blade down each side of the nut so it doesn't damage the finger board when lifting the nut straight up. You don't have to go very deep. Just below the surface of the wood. Stops the wood lifting when you remove the nut.

Grab the nut using the wire cutting part with the pliers parallel to the top of the finger board and the ends on the board, preferably with a piece of carboard or such so as not to damage the board and lift straight up. Don't have to worry about misguided hammer strikes or damaging the side of the board or neck with the bit you are using to strike the nut.

Have used this method on all my guitars without a worry.