I have a mandevilla growing on a trellis in a large pot that I need to bring it yet. Like you I have been keeping it outside during the daytime. Last time I tried to keep one it didn't survive. Maybe I threw it out too soon as I didn't know that it could lose all its leaves. I am going to try again using pvick's suggestion.

Here is a link with pvick's info on mandevilla. She grows all her plants in pots on her balcony and has experience overwintering mandevilla. The subject is storing dahlia and canna tubers. pvick's note is about half way down.

Hope they do well for you.
Bobbie

Here is a link that might be useful: storing bulbs and tubers