To delete a category from a website
Use the Delete Categories button on the Content Categories toolbar to remove categories from a website. If you delete a root category, all of its subcategories are deleted as well. You cannot delete a category that is in use. Specifically, you cannot delete a category that backs an existing field in a Poll, in another Web form, or in the Properties step of a content type. Therefore, you cannot delete a category defining a content filter, since the filter itself depends on a category-backed field in the Properties step that authors use to categorize an item. If you try to delete a category that is in use, an error message appears, such as: "You cannot delete the category Cities because it is associated with the field City of the content type Press Release
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Go to the Content Categories interface for the desired website (host).
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In the left pane, highlight the root category of the subcategory you are deleting.
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In the right pane, select the subcategory you wish to delete.
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Click the Delete Categories button.