The process of removal of wastes is called excretion. Humans have a separate system that takes care of the process of removing wastes from the body. Excretion in plants is not very complex as they do not have separate organs for the same.
Photosynthesis and respiration are two the important processes happening in plants. In the process of photosynthesis green plants form simple sugars in the presence of sunlight. As a part of the reaction, they release oxygen into the atmosphere. Oxygen produced as a result of photosynthesis, gets used up by the plants during respiration. Carbon dioxide gas produced as a result of respiration is used up during photosynthesis. Thus, the waste released by both photosynthesis and respiration are used up by each other.
Leaves have tiny pores called stomata and stems have pores called lenticels through which excess gaseous wastes are sent out. Also trees shed their leaves and barks, some of the wastes that got accumulated get eliminated. Some waste products are actually stored in the plant body as solids. Rap hides, tannins, resins, gum, rubber and essential oils are some such wastes.