GRUB is not a Linux bootloader, but it has to keep its files somewhere, and that is usually on a partition of the distro that installed it, so deleting that partition with render GRUB unusable. If you want to switch one distro for another, the simplest option is to install the new distro over the top of the old one - its installer with reformat the old partition and then install the distro, along with GRUB, so your system will still dual boot.
Most installers have an option to replace another distro with the new one. If not, just tell it to install to whichever partition(s) your old distro used.
"Insanity: doing the same thing over and over again and expecting different results." (Albert Einstein)