When operating the air conditioner the car will cut off?

Hello,

This issue likely due to a faulty idle air control valve (IAC).
When the A/C gets turned on the IAC supped to increase the air flow to the engine and raise the RPMs, when this does not happen the engine can run rough or shut off in some occasions.
The IAC is located on the top part of the engine, side of the throttle body.
You can have this type of issues when the IAC is dirty as well. As the IAC will get dirty with larger air particles overtime and that will restrict air flow thru the valve.
So service the IAC by cleaning it out.

Here are couple of helpful articles:

https://www.2carpros.com/articles/how-a-idle-air-control-valve-works
https://www.2carpros.com/articles/idle-air-control-valve-service

I have attached diagrams for your reference.

Please let me know of any questions.
Thank you.