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While they normally prefer the foliage, it is likely slugs. This article will help:
https://www.gardeningknowhow.com/plant-problems/pests/facts-about-slugs-and-how-to-kill-garden-slugs.htm

In addition to slugs, there are a few caterpillars that enjoy feasting on these plants. Bt can help take care of these pests. Here is more info: https://www.gardeningknowhow.com/plant-problems/pests/using-bacillus-thuringiensis.htm

If it's newly planted, then it may be suffering from shock or there could have be air pockets restricting roots from taking in water. While you could flood the area with water and tamp down around the plants to help collapse any air pockets, right now, you need to determine if the plant is still alive. This article will help with that: https://www.gardeningknowhow.com/plant-problems/environmental/how-to-tell-if-a-plant-is-dead-and-how-to-recover-an-almost-dead-plant.htm

For information on caring for these plants, the following article should help: https://www.gardeningknowhow.com/ornamental/flowers/chrysanthemum/growing-chrysanthemum-flowers.htm
https://www.gardeningknowhow.com/ornamental/flowers/chrysanthemum/wintering-mums.htm

Chrysanthemums are day length sensitive, meaning when there are a certain number of daylight hours the mum will bloom. Some need long days others shorter. Few mums will actually list the day length on the label. So it's pretty much trial and error. I like to swap with friends to get the kinds I actually want.

This article should help: https://www.gardeningknowhow.com/ornamental/flowers/chrysanthemum/wintering-mums.htm

It sounds like you have aphids or mealy bugs. These articles will help:
https://www.gardeningknowhow.com/plant-problems/pests/mealybugs-white-residue-on-plants-leaves.htm
https://www.gardeningknowhow.com/plant-problems/pests/homemade-aphid-control-a-natural-way-to-kill-aphids.htm