An understanding of the missing antinodal electronic excita-tions in the pseudogap state is essential for uncovering the physics of the underdoped cuprate high-temperature super-conductors. The majority of high-temperature experiments performed thus far, however, have been unable to discern whether the antinodal states are rendered unobservable due to their damping or whether they vanish due to their gap-ping. Here, we distinguish between these two scenarios by using quantum oscillations to examine whether the small Fermi surface pocket, found to occupy only 2% of the Brillouin zone in the underdoped cuprates, exists in isolation against a majority of completely gapped density of states spanning the antinodes, or whether it is thermodynamically coupled to a background of ungapped antinodal states. We find that quantum oscillations associated with the small Fermi surface pocket exhibit a signature sawtooth waveform characteristic of an isolated two-dimensional Fermi surface pocket. This finding reveals that the antinodal states are destroyed by a hard gap that extends over the majority of the Brillouin zone, placing strong constraints on a drastic underlying origin of quasiparticle disappearance over almost the entire Brillouin zone in the pseudogap regime.