Set the edge of your grout saw to the surface of the grout you want to extract. Hold the saw at about a 45-degree angle to the surface. Hold the saw handle with one hand, while pressing over the whole back of the saw with the other hand.
Press the saw firmly to the grout and pull it backward, digging into the grout.
Push the saw forward, forcefully, breaking into the grout in front of the blade. Pull it back again and then push further forward, breaking out more of the grout.
Repeat, digging out the grout in a forward-and-back motion, advancing along the whole grout line. Move the blade along the edges of the tiles as needed to extract any grout that’s sticking to the sides of the tiles. Don’t dig any deeper than the tile thickness, which is generally ¼ inch. Dig out each of the grout lines you are trying to extract.
Run your hand-held vacuum along the dug-out line to extract the debris and dust. The tiles are now ready for re-grouting.