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This article should help: https://www.gardeningknowhow.com/ornamental/vines/mandevilla/mandevilla-propagation.htm

All you need to do is trim away any unwanted vines with a sharp pair of pruners. Do not trim away more than 1/3 of the plant.

I would recommend treating the plant with neem oil. This is an effective (and organic) insecticide/fungicide. Here is more information: https://www.gardeningknowhow.com/problems/pests/neem-oil-uses.htm

It is considered in the list of poisonous plants, but allegedly its toxicity is very low, and no severe symptoms would result from ingesting it. However, to be on the safe side, I would try to keep the animals from going near it by adding a barrier or removing the plant.

These plants are normally treated as annuals when planted outdoors where winters drop below 50 degrees F. However, it may be possible for you to dig it up and replant it in a container so that it may be brought indoors for overwintering. You can also sink the container back into the ground once temps rise again in spring.

If the stems are still green and pliable, they will regrow their leaves quickly in the spring. If they are still alive, I would not cut it back. The plant will start to flower when the weather warms up. If the stems are brown and brittle, then they are dead and it would be best to cut them back to the ground (or where ever you see green wood). The stems tend to regrow rapidly when the weather warms up.