You can delete both drafts and published stories.
Be sure that you want to delete a story part, as there is no way to restore it once deleted.
Instead of deleting a part, you also have the option to revert to a draft, so only you can see it.
You can do so by taking the following steps on the browser:
Go to my stories
Select the story and click on the edit button
Scroll down, you will see the Delete story button
Once, you click on it, it will prompt you to click again, asking Are you sure?.