looks like the stop/start battery leaked and stopped working long time ago is it safe to remove it ? I don't want to replace with a new one because I do not want the stop/start feature

 

Yes just remove the small battery. I would tape up the wires just to be sure nothing makes a circuit.
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JaguarXJL15, if you are really worried about the corrosion, take a cup of water (warm) and put in a teaspoon of baking soda. Mix well. You can then go out, disconnect the battery, remove it, then using a brush or paper towel, bribble some water on the connector. It will bubble. That is the baking soda eating up the acid. Put some on, wipe off. Add some more. repeat until no more bubbles. From there, you can dry the terminal, tape it up so you don't have any "random" electrical gremlins running around your car.