SHANGHAI/BEIJING, Aug 25 (Reuters) - China's central bank cut interest rates and lowered the amount of reserves banks must hold for the second time in two months on Tuesday, ratcheting up support for a stuttering economy and a plunging stock market that has sent shockwaves around the globe. The moves came after Chinese stocks tumbled again on Tuesday, as investors despaired at the lack of policy action from Beijing in response to recent data suggesting the downturn in the world's second-largest economy was deepening.