Draw horizontal lines on the baseboard that indicate where the door is going to go.
Cut into the baseboard using a dovetail saw, allowing the pencil lines you made in step 1 to guide you. The strokes you will use are very shallow. Cut from the top of the baseboard to the bottom. At this point, though there are two cuts that separate the segment that needs to be removed, it is still stuck to the wall.
Slide the edge of a utility knife along the top of the baseboard, between the baseboard and the wall. This clears any caulk that was holding the baseboard in place.
Insert the edge of a pry bar into the top of the baseboard and pull the baseboard away from the wall. This takes care of any adhesive or any nails holding the baseboard in place.