I am a foreign resident but a citizen of the USA. I have no US income to report. Do I have to file? I tried to file on turbo tax but they say the amount is too low to e-file and that I have to mail in a return, which is not all that easy from a foreign co

You have to file a US return if your worldwide income meets the filing threshold- it doesn't matter how much was earned in the US. US citizens report their income from anywhere.

The threshold is $10,350 in US dollars (equivalent).

Click begin at the bottom here:

https://www.irs.gov/uac/do-i-need-to-file-a-tax-return 

Also, keep in mind that overseas taxpayers have extra time to file, and the deadline is never particularly relevant if you don't owe taxes.

You probably do need to file. However, you probably don't owe tax or need to worry about getting it done today.

Thank you so much ChristinaS! OK -I figured as much. But then do I need to pay US taxes on foreign-earned money? That doesn't seem very convenient given that my foreign income is already subject to local taxes. If I have to pay taxes in two countries, I would be left with almost nothing........

You enter foreign income under Foreign Earned Income. If you have been abroad, you may qualify to exclude the income from taxes. Or you do the Foreign Tax Credit to get credit for some of the foreign taxes.
You aren't double taxed.

You can't do either in the Free version. You need to upgrade to Deluxe. Federal Taxes-Wages and Income-Less Common Income- Foreign Earned Income and Exclusion.