Spread out a thick towel on a table or workbench.
Place the glass on its side on top of the thick towel.
Put on gloves and safety glasses to protect your hands and eyes from glass shards as you remove the stem.
Fill a spray bottle with plain water. Spray the stem and bottom of the glass with water. This will depress any tiny glass shards while you are cutting.
Score the stem several times with the glass cutter, right under the bottom of the glass. Apply firm but careful pressure to the cutter while scoring the stem with the glass cutter.
Spray the stem and bottom of the glass once again and score around the stem several more times. Your goal is to create a clear, discernible score line between the stem and bottom of the glass.
Pick up the glass by the bottom of the stem and hold the glass over the towel. Gently tap the glass against the towel several times while turning the glass in a circular motion until the stem pops off the bottom of the glass.