Alkaline niobate and tantalate perovskites have attracted attention as polar dielectrics for electronics and telecommunications. Here, we studied the polar behaviour, lattice dynamics, and local structure in conventionally processed K0.985Mn0.015TaO3±δ ceramics using a combination of variable-temperature dielectric and Raman spectroscopies, and X-ray absorption fine structure (XAFS) measurements, respectively. Mn doping induces a low-frequency dielectric relaxation in KTaO3 (KT), which follows the Arrhenius law with an activation energy U ≈ 105 meV and the characteristic relaxation time τ0 ≈ 4.6 × 10−14 s. Our XAFS results support preferential Mn occupancy of the cuboctahedral sites as Mn2+, with these cations strongly off-centred in the oversized oxygen cages. Such disordered Mn displacements generate electric dipoles, which are proposed as the source of the observed dielectric relaxation. We show that in Mn-doped ceramics, the low-frequency polar TO1 mode softens on cooling and, at low temperatures, exhibits a higher frequency than in undoped KT. This mode displays no detectable splitting, which contrasts with Li-doped KT that also contains off-centred Li+ species on the cuboctahedral sites. Therefore, we conclude that the coupling between the Mn displacements and the lattice is weaker than in the Li case, and Mn-doped KT therefore exhibits a dielectric relaxation but no ferroelectric transition.