Yes there's a Settings category called 'Automatic cleanup' that display some deletion features, but it's only for the downloaded episodes. Only the downloaded file are deleted.
If you don't want to see past episodes in the app, you have to mark the as 'read'. This can be done automatically after the episode as been fully listened to.
You can also do it manually (long press the episode => Mark read) and since the v2.17.4 you can long press an episode and select 'Mark older episodes as Read' in order to apply this flag to all the past episodes.
By default episodes marked as read display a green triangle with a checkbox inside. Then you can press the toolbar Eye icon in order to hide/show read content. You can do this in a screen displaying a list of episodes, but you can also do it in the app main screen. In that case you will only see podcasts having at least one unread episode