When we are saving from our income then we don't consume as mush as we earn. So the GDP should decrease as well as the income but this does not happen. Why?
"GDP" stands for "Gross Domestic Product". It measures the income generated, prior to any consumption-saving allocation. In other words, to be able to save you must first generate product/income and then decide to save. So savings does not affect the level of the already created income, since it is a part of it. The archetypal closed economy with no borrowing is characteriazed by the identity
$$Y = GDP = C + I = C + S$$
When we look the matter from an expenditure approach, we essentially consider the different uses of income (and in that sense the use of the term "expenditure" may be a bit misleading). And savings is also a way to use your income (where "use" has a broader meanign than "spend").