1706, "stoppage of pulse, absence of pulse," from Modern Latin asphyxia "stopping of the pulse," from Greek asphyxia "stopping of the pulse," from a- "not" (see a- (3)) + sphyzein "to throb, to beat violently," which is of unknown origin.
Obsolete in its original sense; the transferred sense of "suffocation, extreme condition caused by lack of oxygen in the blood" is from 1778, but it is a "curious infelicity of etymology" [OED] because victims of suffocation have a pulse for some time after breathing has stopped. Formerly sometimes nativized as asphyxy. Related: Asphyctic; asphyxial.