Choose a rotary tool. A rotary tool allows you to handle small jobs that you couldn't otherwise complete with larger tools. Dremel is known for their versatile rotary tools.
Select a wood cutting attachment designed for making fine cuts to wood. Insert the wood cutting attachment into your rotary tool.
Slide a metal straight edge, such as a ruler or carpenter's square, between the bottom of the baseboard molding and the flooring to prevent accidentally cutting the flooring. Draw two lines down the baseboard where you need to make the cuts.
Turn on the rotary tool and start cutting at the top edge of the baseboard. Start on the outside edge and cut into the baseboard until the cutting attachment sinks all the way through the baseboard. Press the blade down to the bottom of the baseboard. Repeat the process for the other side of the cut.
Cut the caulk line at the top of the baseboard with a utility knife to separate the caulk from the sheetrock. Do not pull the baseboard away from the wall without severing the caulk line, or you may pull away the drywall texture.
Stick a putty knife in between the top of the piece of baseboard and the wall and gently pry it away from the wall. If the piece you've cut does not contain a finishing nail, it will come off immediately and without prying.