Well suffocation which is also known as asphyxia refers to the rapid decrease or complete absence of oxygen in the body and the increase in the presence of carbon dioxide.
When a person is suffocated, the body begins to use up all the oxygen in the blood and organs like the brain which require oxygen to function become deprived of it. The brain uses about 20% of all the oxygen in the body at a particular period of time because it requires it to metabolize glucose to power the neurons that are in charge of both the voluntary and involuntary actions of the body. When the brain is starved of oxygen, functions like the heart beating begin to shut down and just like the CPU of a computer, once it starts to fail, so does everything else.
At about 30-120 seconds without oxygen in the brain, a person will pass out, at 60 seconds, your brain cells will have already started dying, at 5 minutes your neurons are already pushing up daisy's and permanent brain damage is already at your doorstep.
The brain can at best only survive up to about 10 minutes without oxygen and at that point the amount of anoxic brain damage which the person will have will be irreparable.
It's the lack of oxygen in the brain that will lead to death if a person is suffocated. The brain can still survive for a few minutes after the heart stops, but you'll be clinically dead after a few minutes of suffocation.