Do you know what variety of hydrangea do you have?
The time to prune hydrangeas depends on the type you have - whether it blooms on old wood or new wood.
If your hydrangea has large, round, white flowers in the summer, it is probably Hydrangea arborescens 'Annabelle'. This variety blooms on new wood. H. arborescens cultivars such as 'Annabelle' can be pruned to the ground in the fall or late winter before active growth begins in spring. This promotes large flowers!
If your 'Annabelle' hydrangea tends to flop over from the weight of the flowers like yours are doing, try pruning the stems to 18" - 24" rather than cutting them to the ground. This will allow the stems to thicken and provide stronger support for the large blooms.
Be sure your hydrangea is getting enough sun. Though they can tolerate some shade, if they get too much shade, the stems will be weak and they will not be able to support the weight of the large blooms.
Here is a link with tips on how to prune different varieties of hydrangea.