The energy and the eigenvector of the spin waves in MnTiO3 have been studied as functions of the applied magnetic field using inelastic neutron scattering with and without polarization analysis. It is found that the behaviour depends on the distance q from the antiferromagnetic zone centre: for q congruent to 0 the mode softens completely at the spin-flop field H-sf, but it has finite energy for q > 0; the eigenvector retains its Ising character for small q up to the highest fields measured (5 T = 0.86H(sf), assuming H-sf = 5.8 T), but it changes continuously with held from Ising to Heisenberg character for large q. A very strong, temperature-dependent line width was found at H = 6 T, close to H-sf which is interpreted as further evidence for the soft-mode instability at the spin-flop transition.