Bilayered Sr3Ru2O7 is an unusual metamagnetic metal with inherently antiferromagnetic (AFM) and ferromagnetic (FM) fluctuations. Partial substitution of Ru by Mn results in the establishment of metal-insulator transition (MIT) at TMIT and AFM ordering at TM in Sr3(Ru1-xMnx)2O7. Using elastic neutron scattering we determined the effect of Mn doping on the magnetic structure and in-plane magnetic correlation lengths in Sr3(Ru1-xMnx)2O7 (x = 0.06 and 0.12). With increasing Mn doping (x) from 0.06 to 0.12 or decreasing temperatures for x=0.12, an evolution from an in-plane short-range to long-range double-stripe AFM ground state occurs. For both compounds, the onset of magnetic correlation with an anisotropic behavior coincides with the sharp rise of the electrical resistivity and the specific heat. Since it does not induce measurable lattice distortion, the double-stripe magnetic order with anisotropic spin texture breaks the symmetry from C4v crystal lattice to C2v magnetic sublattice. These observations shed new light on an age-old question of Slater versus Mott-type MIT.