The process of breaking down organic matter into simpler compounds by saprophytic organisms is called:

Decomposition is the process by which saprophytic organisms, also known as decomposers, breaking down dead or decaying organic matter into simpler compounds such as carbon dioxide, water, and mineral ions. 

This process involves the secretion of digestive enzymes that break down complex organic matter into simpler compounds, which can then be absorbed and used as a source of energy by saprophytic organisms.