By default ubuntu-mate comes with a floating gnome- or mate-logo screensaver. You can have your own logo or image as well.
First you need to create a SVG that works on a black background, the default logo is about 128x128, but the size doesn’t matter much. This file can then be placed in /usr/share/pixmaps/ or perhaps more properly /usr/local/share/pixmaps/
In order to make the screensaver, copy /usr/share/applications/screensavers/gnomelogo-floaters.desktop to a new .desktop file in /usr/share/applications/screensavers/
In your new file change the name and comment to fit your new screensaver and most importantly, the exec line.
Exec=/usr/lib/mate-screensaver/floaters /usr/share/pixmaps/gnome-logo-white.svg
The first bit is the ‘floaters’ screensaver, the second bit the path to your new logo.
After doing this you can select your new screensaver in your screensaver-settings menu, or change the default in gsettings, it gets set in ‘/org/mate/screensaver/themes’ and your custom-screensaver.desktop would have the value ‘screensavers-custom-screensaver’.