A tariff, duty, import tax, or whatever you want to call it, is paid by the domestic (US) consumer on the imported good. Out of the price paid by the US consumer for the Mexican product, the sticker price is paid to the Mexican producer, while an extra amount equal to the original price times the tariff rate is paid by the US consumer to the US government.
Why are you sure he will not do that? Could be easily done by an tax on Mexican imports. Didn't you think the Muslim ban was a joke also?