I too am slightly flummoxed. A picture might have been helpful. But if you really do mean chrysanthemums, these dont have bulbs as such - they are mostly herbaceous perennials and have clumps of roots, with rhizomes/stolons if they're hardy. If they are hardy (rather than florist) you would have seen a rosette of leaves on the crown after the'd stopped blooming and could have tried naturalising them in your garden. But chopping the top off wouldnt have helped their chances.
If they are some sort of
spring flowering potted bulbs, I think the usual thing to do is place them in a dark, cool (but above freezing), dry and well ventilated place until autumn. Dont seal them in a box. But if you dont have a convenient storing space inside you might find it better to plant them directly outdoors now and then treat as with any other
spring flowering garden bulb. They might
flower again.