The long-wavelength excitations of a diluted antiferromagnet near the percolation threshold pc are studied. Within the hydrodynamic theory, the excitation frequency depends on two parameters, A and χt. A is the stiffness associated with the spatial variation in the staggered magnetization and χt is the perpendicular susceptibility in the ordered state of the antiferromagnet. The critical behavior of A near pc is known. We develop a field-theoretic formalism to calculate χt. We explicitly calculate χt in the mean-field approximation and find that it diverges as |ln(p-pc)|, as the concentration p approaches pc. Some further scaling arguments yield a scaling relation relating the divergence exponent of χt with other known exponents at the percolation critical point.