Why would China and Russia selling the US' debt ruin the economy? I was listening to an interview with David Harvey and he mentioned that if Russia and China were to sell the debt owed to them by the US, the US economy would take a serious dive. How would they sell the debt and why would that impact the US economy so negatively?
It wouldn't "ruin the US economy". The US (the country as a whole, not the government) bought goods and services from rest of the world by selling them IOUs. So far, the world has been content to let the US roll over these obligations. If the world decided that they wanted to trade these IOUs for goods and services, the US would have to start running current account surpluses and shipping goods abroad to pay for its past current account deficits. These surpluses have to come from somewhere, and they would result in less consumption and less investment in the US economy.

Of course, an economy can't borrow its way in global capital markets forever - the US does eventually have to ship some stuff over to China in exchange for all of the stuff that China shipped over to the US in exchange for (electronic) green pieces of paper. If China decides to unilaterally impose capital controls and stop lending goods to the US, then this hurts both China and the US - the reason capital in China was flowing to the US is that it could get higher returns there. (The functioning of domestic capital markets in China has become a lot better over the past decade, which is why China can now allocate its savings to productive uses domestically instead of lending large amounts of it to foreign countries.) 

What some people are specifically afraid about ties into the USD's status as the international reserve currency - the Chinese government and central bank own plenty of US government debt as part of their foreign exchange reserves, and if they want to redeem this debt in exchange for goods and not roll it over, the scenario I mentioned above comes to pass. This seems to me like a grossly exaggerated concern at a time when global real interest rates are quite low. If China wanted to sell its US government bonds and the US had no intention of stopping the rollover process, returns would rise until the market for US external debt cleared, and there's no reason to think that the return response would be large given the low level of global real interest rates. The US (as a country) would have to pay more interest on its debt outstanding, which isn't great, but it's not a disaster of a scale that would "ruin the US economy".