We're exempt on tax on "Earned Income" up until a certain level (and yes, there is a highly technical definition for the type of income that qualifies for this). As one of the other commenters mentioned, we still have to pay full on Social Security, Medicare, Self-Employment taxes
If you live in one of the 24 countries with a social-security totalization treaty (which is most of Europe, plus Japan and a few other countries), that's not true. I don't pay any U.S. payroll taxes as an American expatriate.