Unfortunately if you are an American, unless you renounce your citizenship (which is almost certainly more trouble than it's worth), you are required to pay taxes regardless of whether or not you are living in the US. Even if you are paying taxes as someone living in and running a company in another country, you're still required to be paying taxes to the US.

AFAIK, the US is one of, if not the only country, with such rules. It's ridiculous.