We consider simplified dark matter models where a dark matter candidate couples to the standard model (SM) particles via an $s$-channel spin-2 mediator, and study constraints on the model parameter space from the current LHC data. Our focus lies on the complementarity among different searches, in particular monojet and multijet plus missing energy searches and resonance searches. For universal couplings of the mediator to SM particles, missing-energy searches can give stronger constraints than $WW$, $ZZ$, dijet, dihiggs, $t\bar t$, $b\bar b$ resonance searches in the low-mass region and/or when the coupling of the mediator to dark matter is much larger than its couplings to SM particles. The strongest constraints however come from diphoton and dilepton resonance searches. Only if these modes are suppressed, missing-energy searches can be competitive in constraining dark matter models with a spin-2 mediator.