How to remove all items from Steam store cart?

As of now the Steam cart has a "Remove all items" link by default, so no tricks are necessary anymore.

Old answer:

Separate store sessions seem to have separate carts as well, meaning if you add an item within the steam app it will not show up in the cart when you log in with a browser.

Sadly this means Private Pansys answer won't work for the cart in the steam app.

The only way I could find was to clear the cookies of the steam integrated browser:

This will also clear some other settings, like the age you entered for the +18 games, but IMO that's a small price to pay.

Enhanced Steam has this feature. To use it, log into Steam from your browser, and install the extension from its homepage. Restart your browser if necessary, and you should see the 'Empty Cart' button on the Steam cart page.