No, you're not missing it. Other feed readers often force you to manually delete items but Awasu takes care of it automatically for you by letting you configure how long you want to keep stuff for (it gets deleted automatically after that amount of time passes).
You also have fine control over which items get shown when you open a channel (e.g. only new items, only unread ones, only stuff from the past 3 days, etc.) so you don't have to see things you've already read if you don't want to.