can i disconnect battery 2013 cooper S N18 to do work on the car

Nope, you need a memory saver tool. It hooks up to the OBD 2 port and uses an isolated power supply. Mine uses a motorcycle battery and is good for well over a week.

If you disconnect the battery at all, you risk losing the car's computer memory and the need to have that replaced by you and by the car's drive experience. Or it might necessitate a dealer to redo the basic memory..... To maintain power to the car, you could use a simple and inexpensive memory saver. Or as I've done for decades, Have a donor battery or a donor car and run jumper cables to the battery cables. With this, you're just replacing one battery's power with another.