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Yes, there are several places online where you can buy seeds. Be aware though that plants grown from seed may take longer to bloom than those grown from cuttings.

This article will help you with understanding more about pinching plants: https://www.gardeningknowhow.com/garden-how-to/info/pinching-plant.htm

Garden mums are not as hardy as nurseries would like people to believe. They have a hard time surviving the winter and you can expect about a 50/50 chance of them surviving regardless of what you do. You trimmed them correctly. It was the winter cold that killed them.

Usually, these plants are cut back in the fall following a few frosts. Stems of mums are pruned back to 3-4 inches above the ground. New growth appears from this in spring. If you are not able to cut the plant back in fall, you can do so in spring if there is still old, dead growth present. I would not trim off the new green growth.

If they are in pots, place them in a cool, dark place. Water them about once a month until spring. In early spring, resume normal watering and bring them out when the last frost has past. For those outdoors (in ground), trim to ground and mulch well. This article may also help: https://www.gardeningknowhow.com/ornamental/flowers/chrysanthemum/wintering-mums.htm

In case you're uncertain about their survival, you can also take cuttings from them. Here is more information: https://www.gardeningknowhow.com/ornamental/flowers/chrysanthemum/mum-propagation.htm

It may be better to grow additional plants from division or cuttings rather than the seeds. Here is more information: https://www.gardeningknowhow.com/ornamental/flowers/chrysanthemum/mum-propagation.htm

You can pinch back nearly any type of plant such as annual flowers, vegetables, herbs and late-blooming perennials. Here is an article that you may find helpful: https://www.gardeningknowhow.com/garden-how-to/info/pinching-plant.htm