Sounds to me like these mums had some kind of disease, or they were just about finished blooming. Without seeing them it is hard to tell. Do they still have buds. If they have buds and the plants are still green then yes pick off the dead flowers.

Perennial mums would do great in your area, and come back every year.

I have purchased Chrysanthemums, that died down after transplanting outside but came back next spring. If space, inclination and the like permit my suggestion would be to water them occasionally unless you get an occasional snow or rain and then start treating them serious next spring.

I vaguely recall they emerge slowly and fairly early in the spring.

I suspect you are buying the ones found at this season and those aren't 'annual' mums, but perennial ones. A lot of vendors shy away from calling them perennials, because many folks do not have good luck with them returning, but they're perennials, nonetheless.

When you buy a fall mum, try to get them before they're into full bloom. They have a specific and limited bloom span, so you'll want them just showing some colour and in bud.

The market is flooded with growers now, and some aren't well grown to begin with. IOW dead men walking. But, if your's started out healty, you are probably just at the end of their bloom season and they'll be back next spring, if they're healthy and happy where you put them.