iTunes is storing backups by default on local (system) hard drive. That takes heaps of space, so the external HHD would be better choise.
To prevent this from happening, a symbolic link has be to created and point onto a folder in external hdd.
Following command in a terminal will do the trick.
ln -s /Volumes/1TB/Backup ~/Library/Application\ Support/MobileSync/
Just note the following:
1TB = name of external hdd (if it has spaces, then use “1TB”)
Backup = folder on external HDD
MobileSync = does not have folder “Backup” prior running the command
PS: this is general procedure, which might differ based on version of iOS, especially location of backup files on local hdd. Tested on macOs Sierra 10.12.4.