There are 3 main reasons for cutting the stem:

To protect themselves from drying out, plants and trees drop their buds, blooms and leaves. For cut flowers and potted plants this dropping is often the result of over-production of the growth hormone ethylene; the only known gaseous, naturally occurring plant growth hormone. Ethylene gas regulates the ripening/ageing of cut flowers, potted plants, fruits and vegetable fruits. Ethylene gas is therefore purposely used to promote the ripening of fruit and the blooming of potted plants.

Leaves contaminate the vase water, just like stems do. The stem has to be in the water; the leaf, however serves no purpose in the water, in fact, it has a negative effect! Therefore, it is recommended to remove the lower which would otherwise be in the vase water. The additional positive effect of this is that it decreases the amount of evaporation because the total leaf surface is decreased.