In Startup Applications, click on the application you don't want to be open at the startup then click on remove button on the right. This doesn't unistall the app, only disable the application opening on startup. In alternative you may uncheck the chekbox on the left of the application name, it works too and you can reactivate the application at startup whenever you want easily.
if Plank doesent appear in startup application try:
sudo sed --in-place 's/NoDisplay=true/NoDisplay=false/g' *.desktop
It should show all deamons at startup, also the system one.
with MATE Tweak go to interface->pannels and in the first select you should have selected Cupertino that has plank by default, now select MATE and plank should disappear