Thanks for your help, James. I re-explored the theme options and was able to get closer to what I wanted, at first these did not have the effect I desired.
remove_action ('commerce_after_shop_loop_item', 'superstore_product_loop_categories', 2 );
This didn't seem to do anything, but somehow I have managed to remove the categories anyway (I had better figure out how! - I think it was through custom css).
The second remove action works, but I would like to keep the PRODUCT DESCRIPTION tab. What I am looking for is to remove the tab title, it's appearing twice on my product page. I only want it to appear once. Is there a way to remove the second one? (it's an h2 tag)