Isn't there any backup software which keeps deletion information
Robocopy /mir will delete the files that you have deleted from your source, from your (full) backup.
What I understand about mirroring utilities is, they mirrors the entire source time & again. That redundancy will waste my disk space for no good reason.
If you have just one backup location, and you always use /mir, you'll have just one backup copy. Robocopy skips the existing files which have not changed, so the operation is fairly quick. I have about 200gb backed up to usb2 hard drives, and if no files have changed the backup takes 3 minutes.
Having just one backup copy is perhaps not ideal though, so you could use robocopy /maxage first to make a separate backup of new or altered files to a separate location, and keep a few of these incremental copies.
In a previous employment I used backup exec and arcserve, but a couple of usb hard drives and a robocopy script ended up being far more useful.