Mysql allows you to run queries that apply to all post, see example :
UPDATE wp_posts SET POST_CONTENT = replace(POST_CONTENT, '<a href="http://mysite.com/my_link">mylink</a>', '');
This code allows you to delete <a href="http://mysite.com/my_link">mylink</a>on all posts. But in your case I doubt all links are the same so you need a pattern. Perhaps it can be done with [REGEXP].1
Do you need to delete all links in content? That would be easier.
EDIT: make a backup of your database before anything !