Pinocytosis and phagocytosis are both types of endocytosis. Pinocytosis is cellular drinking and phagocytosis is cellular eating. Here is a site that I found very useful when learning about the cell membrane and types of transport across it.
Pynocitosys is a form of endocitosys. this basically means that through this process things go in the cell and not out. So, as an answer to your question, no substances can be eliminated through pinocitosys. the ways of eliminating substances are various depending on the organism(difusion, contractile vacuola etc)