If you installed LMDE and you don't like/need MATE, or you only want to use Cinnamon, then I suggest you read on.

{P.S. part of this tutorial is recommended only if you've upgraded your system' packages to the latest version, or if you have very good understanding of the upgrade process, a.k.a if you know what you're doing)

To completely remove MATE DE off of your computer, log in to Cinnamon, open Terminal and paste this command below: 

sudo apt-get purge notification-daemon+ atril caja caja-common engrampa engrampa-common eom eom-common ffmpegthumbnailer-caja libatril libcaja-extension libmate libmate-common libmatecanvas libmatecomponent libmatecomponentui libmatedesktop libmatekbd libmatemenu libmatepanelapplet libmatepolkit libmatesensorsappletplugin libmateui libmatevfs libmateweather libmateweather-common mate-applets mate-applets-common mate-backgrounds mate-calc mate-conf-editor mate-control-center mate-core mate-desktop mate-desktop-common mate-desktop-environment mate-indicator-applet mate-keyring mate-media mate-menus mate-mime-data mate-netspeed mate-notification-daemon mate-panel mate-panel-common mate-polkit mate-power-manager mate-power-manager-common mate-screensaver mate-sensors-applet mate-session-manager mate-settings-daemon mate-settings-daemon-common mate-settings-daemon-gstreamer mate-system-monitor mate-system-tools mate-terminal mate-text-editor mate-themes mate-utils mate-vfs mate-vfs-common mate-window-manager mozo python-mate python-mate-desktop python-mate-menu

P.S.: To ensure that your system is clean from leftover dependecies, I suggest installing "upgrade-system" package and running it (sudo upgrade-system). Do that only if you know what you're doing because that program will also upgrade all installed packages on the latest version found in the repositories. Breakages may occur! {Use at your own risk}