Using high-resolution inelastic neutron scattering, we examine the spin dynamics of Mn1−xCoxWO4 in the collinear AF1, the ac-b spiral AF2, and the ac cycloidal AF5 phases. The spin wave excitations are well described by a Heisenberg model with competing long-range exchange interactions (Ji up to 12 th nearest-neighbors) and the single-ion anisotropy K induced by the spinorbit interaction. While the exchange constants are relatively unchanged, the dominant effect of doping is to change the single-ion anisotropy from easy axis (K > 0) in the collinear AF1 phase to easy plane (K < 0) in the two multiferroic phases.