Your Previous Post list will show you all posts which have been published or exported from the Studio app.
Deleting a Previous Post
Within the Studio App, there is no option to remove a previous post- the post would always display under the "Previous Post" section.
You can however remove a post completed by the Studio app directly within your social platform. You would login to that social platform and DELETE the post from you social account directly (noting the org. post will always stay documented within your Studio app under 'Previous Posts').
Step by step instructions on removing a post for the following:
Related articles, review deleting a scheduled post.