Neutron scattering is used to study spin waves in the three-dimensional Heisenberg ferromagnet YTiO3, with spin-spin exchange disorder introduced via La substitution at the Y site. No significant changes are observed in the spin-wave dispersion up to a La concentration of 20%. However, a strong broadening of the spectrum is found, indicative of shortened spin-wave lifetimes. Density-functional theory calculations predict minimal changes in exchange constants as a result of average structural changes due to La substitution, in agreement with the data. The absence of significant changes in the spin-wave dispersion, the considerable lifetime effect, and the reduced ordered magnetic moment previously observed in the La-substituted system are qualitatively captured by an isotropic, nearest-neighbor, three-dimensional Heisenberg ferromagnet model with random antiferromagnetic exchange. We therefore establish Y1−xLaxTiO3 as a model system for the study of antiferromagnetic spin-exchange disorder in a three-dimensional Heisenberg ferromagnet.