Death scythes from my understanding have the function of removing ones soul or essence of existence. Doing so conventionally kills the victim.
It should not be used in any other way than reaping people from the list. But Grell in particular is not a shinigami that follows the rules as he steps out often on a whim for adventure and excitement.
This is shown in several points in the jack the ripper arc in which case he is immediately brought back to HQ for disciplinary action.
The more notable thing that occurs is when the scythe is used on demons and zombies. But that is thoroughly explored in later chapters of the manga.
In short spoilers below :
Demons don't have records because they are darkness, evil beings that were not alive to begin with. And zombies have content even if their record stopped recording. These are noted out towards the end of the jack the ripper arc and in the beginning of the emerald witch arc.