Supondo que você instalou usando o PPA referenciado aqui , você pode remover o Cinnamon junto com suas dependências usando os seguintes comandos:
sudo apt-get install ppa-purge
sudo apt-get purge --auto-remove cinnamon
sudo apt-get autoremove
sudo ppa-purge ppa:gwendal-lebihan-dev/cinnamon-stable
Para remover o Xubuntu-Desktop e seus pacotes associados:
sudo apt-get remove abiword abiword-common abiword-plugin-grammar abiword-plugin-mathview bison blueman brltty-x11 catfish elementary-icon-theme exo-utils flex gigolo gimp gimp-data gmusicbrowser gnome-icon-theme-full gnome-system-tools gnome-time-admin gnumeric gnumeric-common gnumeric-doc gstreamer0.10-gnomevfs gthumb gthumb-data gtk2-engines-pixbuf gtk2-engines-xfce indicator-application-gtk2 indicator-messages-gtk2 indicator-sound-gtk2 indicator-status-provider-pidgin leafpad libabiword-2.8 libaiksaurus-1.2-0c2a libaiksaurus-1.2-data libaiksaurusgtk-1.2-0c2a libao-common libao4 libaudio-scrobbler-perl libbabl-0.0-0 libclutter-1.0-0 libclutter-1.0-common libclutter-gtk-1.0-0 libcogl-common libcogl5 libconfig-inifiles-perl libencode-locale-perl libept1 libexo-1-0 libexo-common libfile-listing-perl libfont-afm-perl libgarcon-1-0 libgarcon-common libgdome2-0 libgdome2-cpp-smart0c2a libgegl-0.0-0 libgimp2.0 libglade2-0 libgnomevfs2-extra libgoffice-0.8-8 libgoffice-0.8-8-common libgsf-1-114 libgsf-1-common libgstreamer-perl libgtk2-notify-perl libgtk2-trayicon-perl libgtkmathview0c2a libhtml-form-perl libhtml-format-perl libhtml-parser-perl libhtml-tagset-perl libhtml-tree-perl libhttp-cookies-perl libhttp-daemon-perl libhttp-date-perl libhttp-message-perl libhttp-negotiate-perl libid3tag0 libido-0.1-0 libilmbase6 libio-socket-ssl-perl libjpeg-progs libkeybinder0 liblink-grammar4 libloudmouth1-0 liblwp-mediatypes-perl liblwp-protocol-https-perl libmad0 libmailtools-perl libnet-dbus-perl libnet-http-perl libnet-ssleay-perl liboobs-1-5 libopenexr6 libotr2 libots0 libpolkit-gtk-1-0 libsexy2 libtagc0 libthunarx-2-0 libtie-ixhash-perl libtimedate-perl libtumbler-1-0 liburi-perl libwv-1.2-3 libwww-perl libwww-robotrules-perl libxfce4ui-1-0 libxfce4util-bin libxfce4util-common libxfce4util4 libxfcegui4-4 libxfconf-0-2 libxml-parser-perl libxml-twig-perl libxml-xpath-perl libxss1 lightdm-gtk-greeter link-grammar-dictionaries-en m4 mpg321 murrine-themes orage parole pastebinit pidgin pidgin-data pidgin-libnotify pidgin-microblog pidgin-otr plymouth-theme-xubuntu-logo plymouth-theme-xubuntu-text python-configobj python-glade2 quadrapassel ristretto screensaver-default-images synaptic system-tools-backends tango-icon-theme tango-icon-theme-common tcl8.5 thunar thunar-archive-plugin thunar-data thunar-media-tags-plugin thunar-volman ttf-droid ttf-lyx tumbler tumbler-common xchat xchat-common xfburn xfce-keyboard-shortcuts xfce4-appfinder xfce4-cpugraph-plugin xfce4-dict xfce4-fsguard-plugin xfce4-indicator-plugin xfce4-mailwatch-plugin xfce4-mixer xfce4-mount-plugin xfce4-netload-plugin xfce4-notes xfce4-notes-plugin xfce4-notifyd xfce4-panel xfce4-places-plugin xfce4-power-manager xfce4-power-manager-data xfce4-quicklauncher-plugin xfce4-screenshooter xfce4-session xfce4-settings xfce4-smartbookmark-plugin xfce4-systemload-plugin xfce4-taskmanager xfce4-terminal xfce4-utils xfce4-verve-plugin xfce4-volumed xfce4-weather-plugin xfconf xfdesktop4 xfdesktop4-data xfwm4 xfwm4-themes xscreensaver xscreensaver-data xscreensaver-gl xubuntu-artwork xubuntu-default-settings xubuntu-desktop xubuntu-docs xubuntu-icon-theme xubuntu-wallpapers
Para remover o Lubuntu-Desktop e seus pacotes associados:
sudo apt-get purge --auto-remove abiword abiword-common abiword-plugin-grammar abiword-plugin-mathview ace-of-penguins audacious audacious-plugins audacious-plugins-data blueman chromium-browser chromium-browser-l10n chromium-codecs-ffmpeg elementary-icon-theme esound-common galculator gdebi gdebi-core gecko-mediaplayer giblib1 gnome-icon-theme-full gnome-mplayer gnome-system-tools gnome-time-admin gnumeric gnumeric-common gnumeric-doc gpicview gtk2-engines-pixbuf guvcview hardinfo indicator-status-provider-pidgin leafpad libaacs0 libabiword-2.9 libaudclient2 libaudcore1 libaudiofile1 libbinio1ldbl libbluray1 libbs2b0 libcddb2 libcompfaceg1 libcue1 libencode-locale-perl libept1.4.12 libesd0 libexo-1-0 libexo-common libexo-helpers libfile-listing-perl libfluidsynth1 libfm-data libfm-gtk-data libfm-gtk1 libfm1 libfont-afm-perl libgdome2-0 libgdome2-cpp-smart0c2a libglade2-0 libgmlib0 libgmtk0 libgmtk0-data libgoffice-0.8-8 libgoffice-0.8-8-common libgringotts2 libgsf-1-114 libgsf-1-common libgtkmathview0c2a libguess1 libhtml-form-perl libhtml-format-perl libhtml-parser-perl libhtml-tagset-perl libhtml-tree-perl libhttp-cookies-perl libhttp-daemon-perl libhttp-date-perl libhttp-message-perl libhttp-negotiate-perl libid3tag0 libimlib2 libio-socket-inet6-perl libio-socket-ssl-perl libjpeg-progs libjpeg-turbo-progs liblink-grammar4 libloudmouth1-0 liblwp-mediatypes-perl liblwp-protocol-https-perl libmailtools-perl libmcrypt4 libmenu-cache1 libmowgli2 libmpg123-0 libnet-dbus-perl libnet-http-perl libnet-ssleay-perl libobrender27 libobt0 libonig2 liboobs-1-5 libopts25 libots0 libpisock9 libresid-builder0c2a libsidplay2 libsocket6-perl libtar0 libtidy-0.99-0 libtie-ixhash-perl libtimedate-perl libuniconf4.6 liburi-perl libvdpau1 libwebcam0 libwv-1.2-4 libwvstreams4.6-base libwvstreams4.6-extras libwww-perl libwww-robotrules-perl libxfce4ui-1-0 libxfce4util-bin libxfce4util-common libxfce4util4 libxfconf-0-2 libxml-parser-perl libxml-twig-perl libxml-xpath-perl libxss1 lightdm-gtk-greeter link-grammar-dictionaries-en lm-sensors lubuntu-artwork lubuntu-artwork-12-04 lubuntu-core lubuntu-default-settings lubuntu-desktop lubuntu-icon-theme lubuntu-software-center lxappearance lxappearance-obconf lxinput lxkeymap lxlauncher lxmenu-data lxpanel lxpanel-indicator-applet-plugin lxrandr lxsession lxsession-edit lxshortcut lxtask lxterminal mplayer2 mtpaint ntp obconf openbox openbox-themes osmo pcmanfm pidgin pidgin-data pidgin-libnotify pidgin-microblog plymouth-theme-lubuntu-logo plymouth-theme-lubuntu-text python-pysqlite2 python-xklavier scrot sylpheed sylpheed-doc sylpheed-i18n sylpheed-plugins synaptic system-tools-backends transmission ttf-lyx uvcdynctrl uvcdynctrl-data wvdial xfburn xfce-keyboard-shortcuts xfce4-power-manager xfce4-power-manager-data xfconf xfonts-100dpi xpad xscreensaver xscreensaver-data
Para remover o Gnome-Shell / Gnome-Fallback e seus pacotes associados:
sudo apt-get purge --auto-remove alacarte cups-pk-helper gir1.2-accountsservice-1.0 gir1.2-caribou-1.0 gir1.2-clutter-1.0 gir1.2-cogl-1.0 gir1.2-coglpango-1.0 gir1.2-folks-0.6 gir1.2-gdesktopenums-3.0 gir1.2-gee-1.0 gir1.2-gjsdbus-1.0 gir1.2-gkbd-3.0 gir1.2-json-1.0 gir1.2-mutter-3.0 gir1.2-networkmanager-1.0 gir1.2-panelapplet-4.0 gir1.2-polkit-1.0 gir1.2-telepathyglib-0.12 gir1.2-telepathylogger-0.2 gir1.2-upowerglib-1.0 gir1.2-xkl-1.0 gjs gnome-applets gnome-applets-data gnome-contacts gnome-icon-theme-full gnome-panel gnome-panel-data gnome-session-fallback gnome-shell gnome-shell-common gnome-themes-standard indicator-applet-complete libcaribou-common libcaribou0 libclutter-1.0-0 libclutter-1.0-common libcogl-common libcogl-pango0 libcogl9 libgjs0c libmozjs185-1.0 libmutter0 libpanel-applet-4-0 mutter-common python-gmenu
Limpar todos os pacotes e bibliotecas .deb desnecessários:
sudo apt-get autoclean
Verifique se todas as dependências de pacote ainda estão intactas (ao atualizar seus pacotes existentes):
sudo apt-get update && sudo apt-get dist-upgrade