We report inelastic neutron scattering results that reveal an hour-glass magnetic excitation spectrum in La1.75Sr0.25CoO4. The magnetic spectrum is similar to that observed previously in La1.67Sr0.33CoO4, but the spectral features are broader. We show that the spectrum of La1.75Sr0.25CoO4 can be modeled by the spin dynamics of a system with a disordered cluster spin glass ground state. Bulk magnetization measurements are presented which support the proposed glassy ground state. The observations reiterate the importance of quasi-one-dimensional magnetic correlations and disorder for the hour-glass spectrum, and suggest that disordered spin and charge stripes exist at lower doping in La2-xSrxCoO4 than previously thought.