Take the bridges. It's basic military strategy. You take the bridges out and then you leave each part stranded from the other. No aid, no food, no transfer of resources. Speeds up the inevitable conquest, for a rapid and efficient end to the siege.
Some are tougher than others to crack, of course. Some just take a petrol bomb to knock out. Bloody impressive sight, that. I love the sight of a burning bridge in the morning. Really good for crushing morale. Some, of course, take a more concerted effort to put into the water. But when they go, my God is that satisfying. Few things more satisfying in this life, to see your days and weeks of effort rewarded like that.
Take the bridges. Unpick the stitches that this community wove for itself to unite and grow together, and you will divide them. Then, when you're the only one with access to all sides, you become the one with Aid, with Food, with Resources. Siege ended. Conquest complete.