Make a straight line on the baseboard using a pencil to indicate where you'll make the cut. Place a level on the baseboard, and trace along the edge if you need to make long lines.
Place the tip of a nail set tool on each nail head that lands on the cut line. Hit the back of the nail set tool with a hammer to push the nail through the baseboard so that it doesn't damage the saw blade.
Equip an oscillating tool with a flush-cut blade made to cut wood. Check the oscillating tool for any defects that could hinder its use, such as a frayed power cord or a cracked motor housing.
Line up the oscillating tool's blade with the cut line visually, and squeeze its power trigger. Allow the blade to oscillate at full speed before plunging it into the wood baseboard.
Moving in a slow forward direction, cut the indicated line on the baseboard while keeping the oscillating saw stable.