winter garaged Mandivilla vine has black spots on the new leaves
how can I identify and treat the cause?
This sounds like it could be the start of a fungal or bacterial infection. For general care of this, as long as it is one of the many curable issues, and not an incurable one, is to apply wettable sulfur and dolomitic lime to the soil. You can also add a little peroxide with your water when you water.
Here is an article for proper care of these: https://www.gardeningknowhow.com/ornamental/vines/mandevilla/mandevilla-plant.htm