Should I cut back tropical milkweed?

If you're in a continuous growing region or bring plants indoors to overwinter...Yes! it's important to cut back foliage/stems so fresh growth can emerge and monarch-killing pathogens won't build up on plants. 

You can stagger cuttings (cut back most now, a few later) so you always have some milkweed available for monarchs.

Tropical Milkweed Problems and Solutions