How to back up saves? Just go into your save folder, and copy-paste them to another location! That way you've got two copies of them so you can delete the old version safely.
'cause uh, yeah, just deleting the old version isn't going to work in this case! You actually need to move them across yourself! The save file transfer guide is included in the download which has the same instructions in it too, so don't forget to look at that as well!