If you need to remove any or all of the products links within a Magento installations.
Simply use phpmyadmin to empty the relevant tables. Use the following SQL queries on catalog_product_link.
Don’t forget to back up your database!
Please note check that the IDs match with your installations. i.e. that 1 actually is Related Products as they may not always be the same accross installaions and versions.
For Related Products:
DELETE FROM `catalog_product_link` WHERE `link_type_id` = 1;
For Up-Sell Products:
DELETE FROM `catalog_product_link` WHERE `link_type_id` = 4;
For Cross-Sell Products
DELETE FROM `catalog_product_link` WHERE `link_type_id` = 5;