The Dark Mummy is a monster that only spawns in Hard Mode after you have defeated the Wall of Flesh. They drop coins and occasionally (10% chance) a Dark Shard on death. With the Dark Shard you craft the Dao of Pow. Dark Mummies can be found in the Corrupted Desert. When damaged, they will run faster. Despite the fact that they look similar, this isn't to be confused with the Light Mummy, which is its alternative, found in the Hallowed Desert.
The Dark Mummy is actually quite a fast moving mob, and may be tough to evade. In addition to its speed, it can hit roughly 60 damage, with good defense, and so it's recommended to keep your distance.
You can also make an artificial Corrupted Desert with 750 ebonsand therefore allowing them to spawn.