Some animals Are Eating my Mums!
We cannot say for sure what you are dealing with. In general, deer seldom damage mums but if hungry enough they will eat anything. Keep in mind that deer may browse on any new plantings even resistant plants until mature. Rabbits are not picky about the flowers they eat.
Moles are not the culprits. They feed on soil insects like earthworms and grubs.
There are no easy solutions when it comes to wildlife. You will have to provide protection. Protect the plants with repellents or deer netting/fencing. If you have to rely on repellents, they will have to be reapplied as they wear away in the elements. It also helps to rotate the repellents as deer can get used to them.
Also, squirrels may be a culprit as they tend to dig in containers and may uproot plants. It is possible they may feed on the flowers too.