  High-energy muon collider can play as an emitter of electroweak gauge bosons
and thus leads to substantial vector boson scattering (VBS) processes. In this
work, we investigate the production of heavy neutral lepton (HNL) $N$ and
lepton number violation (LNV) signature through VBS at high-energy muon
colliders. VBS induces LNV processes $W^\pm Z/\gamma\to \ell^\pm N \to \ell^\pm
\ell^\pm W^\mp\to \ell^\pm \ell^\pm q\bar{q}'$ with an on-shell HNL $N$ at
$\mu^+\mu^-$ colliders. In analogy to neutrinoless double-beta decay with the
HNL in t-channel, the LNV signature $W^+W^+\to \ell^+\ell^+$ can also happen
via VBS at same-sign muon collider. They provide clean and robust LNV
signatures to tell the nature of Majorana HNLs and thus have more advantageous
benefits than direct $\mu\mu$ annihilation. We analyze the potential of
searching for Majorana HNL and obtain the exclusion limits on mixing $V_{\ell
N}$. Based on this same-sign lepton signature, we also obtain the sensitivity
of muon collider to the Weinberg operator.
