We report the first measurement of differential and total cross sections for the $\ensuremath{\gamma}d\ensuremath{\rightarrow}{K}^{0}\mathrm{\ensuremath{\Lambda}}(p)$ reaction, using data from the CLAS detector at the Thomas Jefferson National Accelerator Facility. Data collected during two separate experimental runs were studied with photon-energy coverage 0.8--3.6 GeV and 0.5-- 2.6 GeV, respectively. The two measurements are consistent giving confidence in the method and determination of systematic uncertainties. The cross sections are compared with predictions from the KAON-MAID theoretical model (without kaon exchange), which deviate from the data at higher $W$ and at forward kaon angles. These data, along with previously published cross sections for ${K}^{+}\mathrm{\ensuremath{\Lambda}}$ photoproduction, provide essential constraints on the nucleon resonance spectrum. A first partial wave analysis was performed that describes the data without the introduction of new resonances.
