1> You can try making a bootable USB thumb/pendrive from that Mandriva's disc image and then >> boot up from that USB drive >> keeping your external hard drive plugged in >> select the appropriate drive/partition during installation.
You can read this article here in order to "how to make a bootable Mandriva 2010 USB drive using Mandriva Seed Box"
2> You can try creating a persistence image of the installation.
i.e. you can simply make a bootable USB pendrive of Mandriva which could run the exact live replica as in Live Disc but it would store/save all the changes made during runtime just like an actual OS installed. :)
You can create this by using any of the following tools:
3> You can try creating the bootable USB pendrive by using LiLi USB Creator (its a free s/w usewd to make bootable pendrives for nearly any linux distro :) )
Universal USB Installer (get it here: pendrivelinux.com/universal-usb-installer-easy-as-1-2-3/) it is as same as LiLi USB Creator. (has a simple GUI not very fancy though :D as in LiLi)