The expected way to install Debian to another partition from within a running Debian system is to use debootstrap. You'll need to format the partition manually and mount it first, then just run
debootstrap with the options to install the Debian version you want along with whatever packages you want (for example,
chroot into it, configure it and install a kernel and some other tools. From your primary partition set up your boot manager (e.g.
grub). Then you should be able to boot into your new partition.