An obsidian knife is a knife made of obsidian. The handle can come in two different varieties. It could be a full one-piece unit based entirely on obsidian or it could be a mix of obsidian and another material for the handle. In ancient times, handles were made of other materials, such as wood. Warriors also used deer antlers for handles.
If the handle is made of different materials, the two parts are usually connected through a primitive mechanism. Simply put, drilling holes into obsidian and fitting a handle the right way may not be the smartest solution. It will lose its hardness, so it becomes more likely to break down. On the same note, it could break while in use and its sharp edges could cause severe injuries.