There are lots of ways to cheat on your taxes. It is called tax evasion. There are also lots of ways to legitimately reduce your tax liability. It is called tax avoidance. How difficult it would be for the IRS to catch you cheating is a completely different topic than the tax liability.
Tracking cash is also hard. An employer could pay all his employees in cash, keep fake books, and cheat on his taxes that way. It doesn't make the tax liability go away. So keep in mind when you are asking a question, which question are you asking.
A US citizen (and in most cases residents) owes US taxes regardless of where the taxable event occurs. It doesn't matter if you leave the US and NEVER come back. The only way to avoid US taxation is to renounce your citizenship (which generally requires you to already have citizenship in another country). Now if you are asking if you could "get away" with traveling to russia to do cash deals for rubbles and then laundering those funds though a bunch of offshore accounts? Maybe but that is asking "will I get caught", not "is this legal". Honestly if it is a small amount of money it probably isn't worth the trouble and if it is a huge amount of money speak to a good offshore lawyer and CPA. Tax avoidance not tax evasion.