Might there be a mis-understanding on your side? “Copy” and “Cut” are different operations. So it’s normal that the copied data resides in the parent table. If you want to delete the source data after it’s being copied, you need to use a Sequence of actions and use a Delete this row action after the data have been copied.
However, as you have noticed it as parent table, I think of a Parent Table and a Child Table where the data is copied and there’s a reference between these 2 tables. Just bear in mind that, if you delete a parent record of a child record, the reference will be lost as well.
You can look at this: