You use the term "mirror image", but what you want to do is not quite a mirror image.
There are 2 types of "backup" you can do of a hard disk.
If you perhaps want to make AN EXACT COPY of your hard disk (or a clone or mirror) then you use a product to CLONE your hard disk. This allows you, for example, to buy a new hard disk, make a clone of the original hard disk onto this new hard disk, and then put the new hard disk in the PC in place of the old one.
This means the NEW hard disk looks like the OLD hard disk and can be put in a computer and you can boot from it.
However what you want to do is make a backup of your whole hard disk (not the same as a clone).
A product like Acronis will take all the files on your hard disk and then "pack" them into one large backup file (or a few smaller ones) to store them onto your hard disk.
You cant boot from this file as it is like a zip file or rar file and only Acronis will recognize it.
When you come to restore from this file you make a Bootable Acronis disk (easy to do) and then boot your computer with the Acronis disk in the PC.
You then select this Acronis file from the external drive and it "unpacks" it and copies it onto your hard drive, overwriting everhthing that is on the disk in the process.
It is important you understand the difference between clone (or mirror) and a full disk backup.