Why the GDP does not decrease even when we are saving from our income?
"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").