If an official organization shuts off the supply of something, they no longer send it to the people they supplied in the past. The State Water Project has shut off all supplies to farmers
If you shut off something such as an engine or an electrical item, you turn it off to stop it working. They pulled over and shut off the engine Will somebody for God's sake shut that alarm off. = switch off
If you shut yourself off, you avoid seeing other people, usually because you are feeling depressed. Billy tends to keep things to himself more and shut himself off