We propose a new beam dump experiment at future muon colliders at TeV energy scales. This provides an opportunity to expand the theory, energy, and intensity frontier of new physics searches. If we were to construct a muon collider, a beam dump would be an economical and effective way to increase the discovery potential of the experiment in a complementary regime. In this work we consider vector models such as the dark photon and Lμ - Lτ gauge boson as new physics candidates. We explore which regions of parameter space can be probed with a muon beam dump. We find that we gain sensitivity in the moderate mass (MeV - GeV) with small to very small coupling.