We study the quasiparticle resonance states near strong impurities in the mixed state of a d-wave superconductor. These states give rise to zero-bias peaks in the local density of states, observed in scanning tunneling microscopy experiments. The field dependence of the peaks is obtained by averaging with respect to the spatially nonuniform Doppler shifts in the energy of excitations. The hybridization of the magnetic-field-induced nodal quasiparticles with the impurity resonances results in the suppression and broadening of the zero-bias peaks. The height of the peaks is found to scale as ${(H}_{c2}{/H)}^{1/2}.$ The magnetic-field response of the peaks is shown to be strongly dependent on the field orientation.