We present a measurement of the total cross section for $\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\rightarrow}\mathrm{hadrons}$, with one photon quasireal and the other a spacelike photon of mass squared $\ensuremath{-}{Q}^{2}$. Results are presented as a function of ${Q}^{2}$ and the $\ensuremath{\gamma}\ensuremath{\gamma}$ center-of-mass energy $W$, with the ${Q}^{2}$ range extending from 0.2 to 60 Ge${\mathrm{V}}^{2}$, and $W$ in the range from 2 to 10 GeV. The data were taken with the TPC/Two-Gamma facility at the SLAC ${e}^{+}{e}^{\ensuremath{-}}$ storage ring PEP, which was operated at a beam energy of 14.5 GeV. The cross section exhibits a gentle falloff with increasing $W$. Its ${Q}^{2}$ dependence is shown to be well described by an incoherent sum of vector-meson and pointlike scattering over most of the observed $W$ range. Agreement at high ${Q}^{2}$ is improved if a minimum-${p}_{T}$ cutoff (motivated by QCD) is imposed on the pointlike contribution.