When you cut a design into a piece of wood or marble, you carve it. Headstone engravers carve people's names and the dates of their births and deaths into gravestones.
You might carve your initials into the tree in your backyard, or carve a walking stick out of a large branch. Some artists work by carving shapes from clay or granite, and a chef learns to carve, or precisely cut up, large cuts of meat and poultry. The Old English root word is ceorfan, "to cut, slay, carve, or engrave."