A data processing system that includes a host system and an external data storage device with an erase before write memory device thereon can be operated by sending a file delete command from the host to the data storage device for one or more files stored thereon. The file delete command may specify a logical address and data to be invalidated associated with the deleted file. The data storage device may identify one or more units of memory allocation in the erase before write memory as containing invalid data based on the specified logical address and data to be invalidated. The data storage device may maintain a data structure that associates physical addresses for units of memory allocation in the erase before write memory with indications of whether the units of memory allocation contain invalid data. The data structure may be used to mark units of memory allocation associated with deleted files as containing invalid data.