Why does the backup file remain even after you remove the source file?

This is the default behavior of Yadis! Backup: it wants to protect you of data loss...
If you accidentally delete a file, you will be able to recover it from your backup (in case it's not in your recycle bin).

Though if you do not like this behavior, you can change it like this:

1) Select your task and press "Edit" in the left side menu bar.
2) Select the "General">"Type" node and choose Task mode "Advanced".
3) Select the "Files">"File Monitoring" node and check the "Process delete events" checkbox.
4) Press the "Save" button at the bottom.