nimas - That's not normal on your car. By your description, it is idling too low. I'm not sure all cars, but most cars are programmed to pick up a bit of rpm when the A/C compressor kicks on.
Here's what I estimate is happening. The bump in rpm causes it to idle more smoothly. And when not using the A/C, the rpm drops too low and the engine is just not balanced very well at that low rpm. But what's causing the low rpm?
I'll tell you what caused the almost identical symptoms as you describe, on my 2003 Toyota Camry. A dirty throttle body. In case you don't know (maybe you do), a throttle body is more or less a tube with a butterfly valve in it. Said valve is controlled by the ECU in our car, and indirectly by your right foot. You push the throttle, the butterfly opens some amount to increase airflow to the engine. At idle, that butterfly is very close to being closed. It only allows a small amount of air to pass by. Just enough air flow to idle the engine at the proper AFR.
In that Camry, I pulled that throttle body out and wow, it was coated with schmutz exactly where air flowed around that butterfly valve at idle. And on the edges of the butterfly where the air flowed past it at idle. I took a toothbrush, paper towels and throttle body cleaner (spray) and sprayed and cleaned that throttle body until it was as clean as possible. Nearly new looking. I put it back in the car and MAN, what a difference. No low idle, perfect throttle response easing away from a stop. It was like the car was new again. All that build up was restricting airflow at idle, and causing the engine to idle low. And at that lower than target idle rpm, the engine wasn't balanced well, and it vibrated badly. All that was gone after I cleaned it.
I'm not saying that's the issue with your Mirage. But the symptoms sound very similar.
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View my fuel log 2020 Mirage ES 1.2 manual: 42.5 mpg (US) ... 18.1 km/L ... 5.5 L/100 km ... 51.0 mpg (Imp)