Inelastic neutron scattering measurements on Ba(Fe0.925Mn0.075)(2)As-2 manifest spin fluctuations at two different wave vectors, Q(stripe) = (1/2,1/2,1) and Q(Neel) = (1,0,1), corresponding to the expected stripe spin-density wave order and checkerboard antiferromagnetic order in the tetragonal I4/mmm cell, respectively. Below T-N = 80 K, long-range stripe magnetic ordering occurs and sharp spin wave excitations appear at Q(stripe) while broad and diffusive spin fluctuations remain at Q(Neel) at all temperatures. Low concentrations of Mn dopants nucleate local moment spin fluctuations at Q(Neel) that compete with itinerant spin fluctuations at Q(stripe) and may disrupt the development of superconductivity.