UPDATE catalog_product_entity_text SET value = REPLACE(value, 'Will_replace_this_text_to_blank', '')

UPDATE catalog_product_entity_text SET value =
    REPLACE(value, 'Will_replace_this_text_to_blank', '')
WHERE attribute_id =
    (SELECT attribute_id FROM eav_attribute WHERE attribute_code = "short_description")
    AND EXISTS (SELECT 1 FROM catalog_category_product WHERE catalog_product_entity_text.entity_id = catalog_category_product.product_id AND catalog_category_product.category_id = {CATEGORY ID HERE});