Hi @howeuth,
all you have to do is mark (right click) the Kali packages for complete removal, as far as Mate goes, simply type "mate" in search and look at the packages that are available.
You can also do a clean install and keep your date files intact if you follow this guide!:
A terminal command (Ctrl + Alt + t) for you that will quickly install almost all of the Mate DE:
sudo apt-get install mate-desktop-environment-core mate-desktop-environment-extras ubuntu-mate-welcome