You can start a new game in Prince of Persia: The Lost Crown by selecting "Start Game" from the main menu and choosing an empty slot.
 
You can have three saved games at a time.
 
Please note that selecting a save slot that is already being used will overwrite the existing file.
 
You can also free up a slot by selecting it, choosing "Delete" and confirming your choice.
 
Your progress for the main campaign and any downloadable content (DLCs) you own is saved to the same save slot.
 
If you would like to restart the main campaign or the DLCs, you can select a different save slot and begin playing again from the start.