Dear student,
As the plants, by the process of photosynthesis, makes food for itself and evolve oxygen as a byproduct of the environment. This oxygen is in turn used by the all the living organism for the respiration.
Cutting down of trees causes deforestation, which reduces the rate of photosynthesis by the plants. So more and more carbon dioxide would start getting accumulated in the atmosphere and level of oxygen get deteriorate. This decrease in the level of oxygen due to cutting down of trees causes a change in the oxygen cycle between plants and living organism.
Regards.