Merging 2 backups - deleted files will stay in the backup

I have this HDD connected to the My Cloud home through the USB interface. Once in a while, I backup the My Cloud home to it and it only backs up the new/modified files that weren’t on the previous backup (the newer backup basically merges with the old one.)
However, when I delete a file on the My Cloud home, it doesn’t disappear on the backup HDD. This can become a problem, since after a while the backup HDD might run out of storage space.

If you need some more explanation, here’s what’s going on.
I have a file on the My Cloud home, that is also on the backup HDD. I delete the file on the My Cloud home and after that, I start a backup. The file is still on the backup HDD, even though it should’ve been gone.