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Transition-metal oxides provide an excellent platform to generate ground states by tuning the various degrees of freedom via stimuli such as chemical doping. By investigating the electrical, magnetic, and thermodynamic properties of several compositions of the bilayered Sr_{3}(Ru_{1−x}Mn_{x})_{2}O_{7} with x ≥ 0.36, we complete its x-T phase diagram and unveil a spin-glass regime. Upon Mn doping, the ground state of the system changes from the short-range antiferromagnetically (AFM) coupled metal (0≤x≤0.05) to the E-type AFM-ordered insulator (0.05<x≤0.20) to the spin-glass insulator (0.20<x≤0.66) to the canted AFM-ordered insulator (x∼1.0). The complex evolution of the magnetic ground state results from the competition between AFM and ferromagnetic (FM) interactions. The peculiar spin-glass state between two long-range magnetically ordered states implies the significance of spin disorder induced by the intermixing of Mn and Ru ions with the lowest transition temperature for Ru : Mn ∼ 1:1 (x∼0.5).