How to backup without including deleted files in the original backup? and more

Not sure about my subject heading but this is what I mean:
Assuming I have:
Text-file-01
Text-file-02
image-file-01
image-file-02
Video-file-01
This-Is-a-Folder 01
This-Is-a-SUBFolder 01

If a full incremental backup is done and then after a while
I add...