A person who works in a cemetery and digs graves is called a gravedigger. The people who do this particular job are also known as burial ground custodians or cemetery workers.
Gravediggers do not generally dig the graves with pick axes and shovels as sometimes portrayed in older movies. They dig graves with excavation equipment such as a backhoe. This shortens the time for digging a grave from eight hours, which is how long digging by hand could take, to 30 minutes. The soil of the grave generally determines the length of the project and the depth of the grave.