What is the damage from nitrous oxide/oxygen deprivation?

Lack of Oxygen: The damage is in the "lack of oxygen" part. The lack of n20 isn't in question here. If too much n20 were to become part of that mixture, reducing the o2 concentration to less than 21%, that could lead to dangerous hypoxemia (lack of o2). This will compromise o2 delivery to your brain and other vital organs, putting them at risk for metabolic failure and even cell death. To be avoided!

Cells need : Oxygen to survive. Depravation of oxygen is the final common pathway to cell damage and death.