At least with the latest version v2.84 The Categories and Tags can be ADDED in bulk to a set of posts but it is not possible to CHANGE, or DELETE, a Category for those Posts.
While Bulk Delete in a WordPress can be done with a Plugin via Bulk Delete (yeah ,everything need plug in at wordpress) The plug in which can be used to delete posts in bulk from selected categories or tags.This Plugin can also delete all drafts, post revisions or pages.Note that this is not what i mentioned earlier REMOVE the selected categories.Instead,it DELETE the posts under the selected categories.
HOW to remove bulk categories from posts without disturbing the existing ones.Some genius actually suggest that we downgrade the wordpress version.
"I used to use an addon called Batch Categories it allowed you to mass remove or add a single category from posts.This addon does not work in 2.7 But I understand that this feature may be already in 2.7.But I cant figure it out anywhere. Basically from what i can tell its all or nothing on the batch category editing in 2.7 ."
"You May have to downgrade to 2.6 and use your Batch Categories plugin to do what you need to do, then upgrade again to 2.7 - yeah, I know, not the best solution."
You can get the plug-in here.
I am not sure that plug-in work in v2.7 but it's not work in v 2.8 which i am using in my other blog. However the new wordpress do provide a option to remove/change the category of the post.There call it" Quick Edit" the solutions is you need to manually editing each individual post ., so it's still manual, but it's something that better then none,not like you have to load up the whole post page to edit the categories.
In short knowing the new wordpress only allows you to add categories to posts in bulk fashion, but not remove categories from posts or overwrite them with something else in bulk will save you a lot of time just try to figure it.
And i suggest you should stop editing your wordpress categories if you are using the latest wordpress.Imagine if you have hundred posts and then being stuck with manually editing them all via Quick Edit. It makes absolutely nonsense to do a bulk update to add a category. Unfortunately, if you have added the new category to replace your previous old category,both will stay there until someone fix the problem.Yeah we appropriate wordpress is a great blogging platform but We would love to have a way to delete ALL posts within a particular category.
The problem has made editing categories in wordpress:one of the Top wasted time Internet programs.
BTW,did you know you can add and remove a label/category in blogger/blogspot in a second without using a single plug-in.