I am working with a huge amount of data and I have to delete a lot of posts and categories through the admin backend. At this moment it is not possible to handle big data in wordpress ! A delete of 4800 posts took me around 8 hours. First I can only delete 200 posts at once, because you are sending the posts with the $_POST data and there is a limit in PHP. For that I suggest to create a filter feature to filter the posts which should be deleted and then submit the delete with a button. the posts which should be deleted can be get through the filter, there is no need to send them by $_POST.
Then each delete of 200 POSTS took a lot of time, I am not sure what is the reason, please check that.
Same with categories - there should be a filter which categories I want see and also should there a filter delete feature. I have there the same problem - to delete 4000 catgegories it is limited through the $_POST request.