Mark a straight line around the bottom end of the rock. Use a rock saw to cut off the rough end and to create a level foot for the vase. Use a water-fed rock saw with a diamond blade. Be careful not to move the rock in other directions as you feed it through the blade as it might shatter the rock, damage the saw, and possibly cause personal injury. Use a grinding wheel or sandpaper to smooth the sharp edges along the cut. Check that the rock is stands without rocking, in the right position.
Lock the rock firmly into a vise, positioning it as it naturally stands. The bottom of the rock should be flush with the bottom of the vise. Clamp the vise securely into place on the drill press table. Line up the rock so that the drill comes down precisely in the middle of the top. Use a smaller starter-bit to begin drilling. Insert a bit about one quarter of the size of the final diameter of the vase opening.
Gently apply downward pressure to the drill. Use a drilling lubricant oil to prevent the bit from overheating. Run the drill at medium speed and adjust it from there. If it overheats, slow it down. Keep drilling until you reach the right depth, at least an inch or two from the bottom of the rock.
Replace the bit with one the next size up and repeat the process. Avoid using too much pressure on the drill to prevent the rock from shattering. Drill to the same depth with each bit to create an even bottom on the inside. Keep the rock placed in the same position throughout the process.
Remove the rock from the vise when finished drilling. Clean the oils from the inside with soap and water. Inspect the vase, and use sandpaper to remove any sharp edges made by the drill at the top of the opening. Sign the bottom to finish the rock vase.