The photo too far away but we believe by the coloration of the underside of the leaf that you have a mite infestation. You might want to take a bagged sample to your local garden center for a more accurate hands-on diagnosis. One of the best options to treat your plant is to remove and dispose of all affected plant parts but we are not sure you are ready for that. Nonetheless, when the plant starts to go dormant in the colder months, be sure to remove all leaf litter that falls from the plant to try to stem the infestation next year. If you are so inclined, you might try treating your plants with Bayer Advanced 3-in-1 insect, disease, and mite control. A straight insecticide is ineffective against mites because they are arachnids.
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Is Neem Oil effective against the mites? The Garden Safe Fungacide3’s only active ingredient is cold pressed Neem Oil, 0.9%. I’ve since bought my own Neem Oil, and mix. The labeling says it’s good against mites, but figured I’d double check.
Also, what does a healthy, but dormant, Mandevilla look like?