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Antiferromagnetic (AF) spin correlations are prominent across the phase diagram of the cuprate superconductors, and it has been proposed that they mediate Cooper pairing and are responsible for various pseudogap phenomena. HgBa₂CuO_4+δ (Hg1201) is a simple-tetragonal compound with a single CuO₂ plane per unit cell and the highest optimal T_c among single-layer cuprates, and thus a model system for the study of the AF response of the quintessential CuO₂ planes. Our previous work has shown that the AF excitations in moderately to optimally-doped Hg1201 are distinctly different from what had been observed in other cuprates; namely, the low-energy response is commensurate and gapped, resulting in a 'Y'-shaped, rather than 'X'-shaped dispersion. Here we present our recent inelastic neutron scattering measurements of the AF excitations in heavily underdoped Hg1201.