Inelastic neutron scattering measurements on Ba(Fe0.925Mn0.075)2As2 manifest spin fluctuations at two different wavevectors in the Fe square lattice, (1/2,0) and (1/2,1/2), corresponding to the expected stripe spin-density wave order and checkerboard antiferromagnetic order, respectively. Below T_N=80 K, long-range stripe magnetic ordering occurs and sharp spin wave excitations appear at (1/2,0) while broad and diffusive spin fluctuations remain at (1/2,1/2) at all temperatures. Low concentrations of Mn dopants nucleate local moment spin fluctuations at (1/2,1/2) that compete with itinerant spin fluctuations at (1/2,0) and may disrupt the development of superconductivity. ; Comment: 5 pages, 5 figures