Spin fluctuations and the local spin susceptibility in isovalently Zn-substituted La\(_{2-x}\)Sr\(_{x}\)Cu\(_{1-y}\)Zn\(_y\)O\(_4\) (\(x=0.25\), \(y\approx0.01\)) are measured via inelastic neutron scattering techniques. As Zn\(^{2+}\) is substituted onto the Cu\(^{2+}\)-sites, an anomalous enhancement of the local spin susceptibility \(\chi^{\prime\prime}(\omega)\) appears due to the emergence of a commensurate antiferromagnetic excitation centered at wave vector \textbf{Q}\(=(\pi, \pi, 0)\) that coexists with the known incommensurate SDW excitations at \textbf{Q}\(_{HK}=(\pi\pm\delta,\pi), (\pi,\pi\pm\delta)\). Our results support a picture of Zn-induced antiferromagnetic (AF) fluctuations appearing through a local staggered polarization of Cu\(^{2+}\)-spins, and the simultaneous suppression of T\(_c\) as AF fluctuations are slowed in proximity to Zn-impurities suggests the continued importance of high energy AF fluctuations at the far overdoped edge of superconductivity in the cuprates.