How to hide the "Add to cart message" on mobile site"?
One way to do it would be to use hook_node_submit to override the submit handler for commerce_cart_line_item_views_form_submit. Check for your theme and apply messages appropriately. However, that will only work for this single message. You would have to rewrite all of the cart functions that have messages.

Another way: I know you can do this with CSS. You just need to target the product pages only. I don't know your CSS structure, but if you look at the classes in the &lt;body&gt; element, you should see classes that you can use to cascade down and set display: none; to the message region. I don't know what other messages will show up that you care about on the product pages. If you do have some, then the first option is your only option. (Or the non-recommended option below.)

You could also edit the cart source but that is not a good option because it breaks your upgrade path.

If you are using Kickstart, I can find the function to override there as well. (I have sites running both.)