Removing products through the database

This should remove all the products and their related records.

  1. TRUNCATE TABLE `catalog_product_entity`;

Removing categories requires bit more actions.

  1. TRUNCATE TABLE `catalog_category_entity`;
  2. DELETE FROM `catalog_category_tree` WHERE `entity_id`<>1;

After that you will have to create root categories for your stores and assign them to stores in configuration:

admin menu / system / configuration / catalog - choose a store, choose Root Category.