I'm not too sure what you are trying to accomplish here. You say you want to clone the table then delete records from each table. Why is it you would like two different sets of records in each table?
If you are simply after deleting records that are no longer required but wish to have a backup if mistakes are made, simply duplicate the database either using the OS or using File -> Save Copy As. Edit the copy file and if you are happy with your record removal switch to using this file. If mistakes have been made you have the original file to fall back on.
If you really want to create a duplicate table, then do as follows:
File -> Import Records -> File
Select your current file even though you currently have it open.
Select Source table to be the one you wish to copy.
Select the Destination table by scrolling to the bottom of the list and selecting New Table. This is defaulted to be renamed TableName2.
All your records will now be duplicated in the new table TableName2
Thanks, the second part of your answer was exactly what I wanted.
I didn't want to delete some of the records, but some of the fields which had gotten to complex for one table, and splitting them across two tables made some relationships a lot simpler.