I've never overwintered a mandevilla so not sure if it's going dormant or truly dying. If it's not in dormancy, I would unfortunately have to say it does look very sick and you may need to prepare yourself that it will probably die (or may even be just about dead) unless something changes fast.

In either case, getting rid of the spider mites is important to give it a chance.

There are many different approaches to fighting spider mites.
I would suggest either soaking the vines in a bucket of water with some dish soap in it or putting it in the shower and thoroughly rinsing off all the leaves (both top and bottom) on a daily basis (try not to get water in the soil though, since overwatering the soil won't help matters).

I'd also suggest getting some neem oil (I like Dyna Gro brand Neem oil) and following the package directions to make up a solution of neem oil, dish soap, and water to spray on the plant every THREE days (I wouldn't use the neem oil every day, because it can potentially harm plants when applied excessively).
I used that neem oil solution to fight off a mild infestation of spider mites on my croton, so I am a fan of neem. Another nice thing about neem is that it is not known to have any harmful effects on humans.

Good luck. Even if you can only keep it just barely alive all winter, I'm sure it will grow by leaps and bounds when it gets to go back outside.

This post was edited by summersunshine on Sun, Nov 9, 14 at 0:22