Both removing & reordering posts that appear in sliders and other lists is a fairly straightforward exercise.
To reorder posts, you can easily drag & drop posts in a specific category via the Posts page of the admin interface. Just select a category in the upper left, and then use the drag icons on the right to drag a post to a new location in the list. See below:
In order to remove a post from a list of posts, you need to edit the post itself. In the screenshot above, you first need to click on the name of one of the posts. This will take you to the “edit post page” for this post, where you can change a post’s status to “draft” in the upper left. All you have to do is click the “Make Draft” link in the upper left, as you can see in the screenshot below.
Alternatively, you can save a post to be used again in the future by moving it to the “Unassigned” category. You can do this by clicking on the “Category” dropdown (circled in red on the right in the screenshot below) and then selecting “Unassigned” from the list of categories.
So there are a couple of options when it comes to removing posts from list of posts, and you can use whichever approach is best for the situation. Either way, the post will no longer appear in the list of posts you’re editing.