  The Weakly Interacting Massive Particle (WIMP) paradigm is one of the most
compelling scenarios for particle dark matter (DM). We show in this paper that
a high energy muon collider can make decisive statements about the WIMP DM, and
this should serve as one of its main physics driver cases. We demonstrate this
by employing the DM as the lightest member of an electroweak (EW) multiplet,
which is a simple, yet one of the most challenging WIMP scenarios given its
minimal collider signature and high thermal target mass scale of 1 TeV$-$23
TeV. We perform a first study of the reach of high energy muon colliders,
focusing on the simple, inclusive and conservative signals with large missing
mass, through the mono-photon, VBF di-muon and a novel mono-muon channel. Using
these inclusive signals, it is possible to cover the thermal targets of doublet
and triplet with a 10 TeV muon collider. Higher energies, 14 TeV$-$75 TeV,
would ensure a $5 \sigma$ reach above the thermal targets for the higher EW
multiplets. We also estimate the reach of a search for disappearing tracks,
demonstrating the potential significant enhancement of the sensitivity.
