I installed MATE environment that I wanted to try out on Debian Jessie along with xfce4, but I didn't like it at all. And then obviously I wanted to remove MATE desktop.

First I found solution on this website, which recommended to use this long command to remove MATE:

sudo apt-get remove atril atril-common caja caja-common engrampa engrampa-common ffmpegthumbnailer-caja libcaja-extension libmarco libmate libmate-common libmatecanvas libmatecomponent libmatecomponentui libmateconf libmatecorba libmatedesktop libmatekbd libmatekeyring libmatemenu libmatenotify libmatepanelapplet libmatepolkit libmateui libmatevfs libmateweather libmateweather-common marco marco-common mate-applets mate-applets-common mate-backgrounds mate-conf mate-conf-common mate-control-center mate-corba mate-core mate-desktop mate-desktop-common mate-dialogs mate-icon-theme mate-keyring mate-media mate-menus mate-mime-data mate-panel mate-panel-common mate-polkit mate-power-manager mate-power-manager-common mate-screensaver mate-session-manager mate-settings-daemon mate-settings-daemon-common mate-settings-daemon-gstreamer mate-system-monitor mate-terminal mate-terminal-common mate-text-editor mate-themes mate-vfs mate-vfs-common mate-window-manager python-mate

But half of those packages were not installed and after unsuccessful try to remove them one by one from the large command, I developed another solution. Below is my shorter version of command to remove MATE from Debian, which perfectly worked for me:

sudo aptitude purge `dpkg --get-selections|grep -E 'mate-|libmate|caja|atril|engrampa|marco'|cut -f 1`

Just copy-paste it to your terminal and hit enter. Now your MATE is completely removed from your system.