ubuntu-mate-desktop is a meta image, it wouldn’t uninstall existing packages. You could give it a test run by installing Ubuntu MATE from scratch, or have Ubuntu Server as a base.
@wimpy wrote how to achieve this with 14.04, instructions for 15.10 should be fairly similar:
Instead of the full desktop, try ubuntu-mate-cloudtop. This looks new, so I suggest giving it a test run first!