Aye you can.
Don't use microsoft though
Use some form of linux.
Make a live OS on a usb stick and set bios to boot from USB first.
Connect external drive and put usb stick in usb port and start.
When the thing has got going copy across to the external everything you want backed up.
Reformat the internal drive but make sure its FAT16 or 32
shut down and disconnect usb and external and set the bios to boot primary drive then DVD/CD then boot with setup disk in the CD/DVD. Use the setup to change the file system to your particular favorite
Install the OS then connect the external and copy the data back.