Why does mixing reactants in different mole ratios affect the amount of the product and the amount of each reactant that is left over?

Because of the reaction stoichiometry (detailed information given below).

Explanation:

Well, reaction stoichiometry determines relationships between reactants and products in a chemical reaction. For example, if the relationship between reactants and/or products is 1 to 1 (e. g. CO + H2O = > CO2 + H2), the product is produced as much as the limiting reactant (s) (which is less than the other one in amount) consumed. For example, if 3 moles CO mixed with 0.5 moles of O2 (so O2 is limiting reactant in this case), 0.5 CO2 and 0.5 H2 are produced and 2.5 moles of CO and 0 moles of O2 (because all of O2 consumed) are left over. So, it can be concluded that the reaction stoichiometry has a direct relationship with the amount of the product and the amount of each reactant left over.