How to delete ALL comments from certain category in WordPress database?

The wordpress database seems fairly straight forward and is extremely well documented:

http://codex.wordpress.org/Database_Description

It seems to me that all the category information is stored in the table wp_term_relationships. So you should select from the comments table, join it with the posts table and then the term_relationships table in order to get the category for each comment.

Something like:

SELECT *
FROM wp_comments
WHERE comment_post_ID
IN (

SELECT c.object_id
FROM wp_terms a, wp_term_taxonomy b, wp_term_relationships c
WHERE a.name="my_category_slug"
AND b.term_id = a.term_id
AND b.taxonomy = 'category'
AND c.term_taxonomy_id = b.term_taxonomy_id
)