  Generation of arbitrarily spin polarized muon pairs is investigated via
polarized $e^-e^+$ collision. We calculate the fully spin-resolved cross
section ${\rm d}\sigma_{e^-e^+\rightarrow \mu^-\mu^+}$ and utilize the Monte
Carlo method of binary collision to describe the production and polarization
processes of muon pairs. We find that, due to the dependence of mixed
helicities on the scattering angle, arbitrarily polarized muon pairs with both
of the longitudinal and transverse spin components can be produced. The
collision of tightly collimated electron and positron beams with highly
longitudinal polarization and nC charge can generate about $40\%$ muon pairs
with longitudinal polarization and about $60\%$ muon pairs with transverse
polarization. The compact high-flux $e^-e^+\rightarrow\mu^-\mu^+$ muon source
could be implemented through the next-generation laser-plasma linear collider,
and would be essential to facilitate the investigation of fundamental physics
and the measurement technology in broad areas.
