Web Master:
I am not sure what is causing the problem. From the photo it appears that the leaves on some branches look very healthy.
I would prune off the dead and sick branches, always prune to above a healthy lateral branch or node, new stems will grow from the node.
Late October is not the best time to be pruning your tree, winter or early spring is the optimal time whilst the tree is dormant. However, given that you tree is looking unwell I would also lightly prune the healthy branches to improve the shape and encourage new growth.
Pomegranate come from the Mediterranean regions with hot dry summers. Like many plants from this area they don't like being over-watered or high levels of humidity and can suffer from fungal diseases. If you can see signs of fungal disease on leaves or buds spray with a copper fungicide after pruning.
Next winter you should prune off some of the older branches to encourage new fruiting growth.