We consider the production of right-handed (RH) sneutrino dark matter in a model of Dirac neutrino where neutrino Yukawa coupling constants are very small. Dark matter RH sneutrinos are produced by scatterings and decays of thermal particles in the early Universe without reaching thermal equilibrium due to the small Yukawa couplings. We show that not only decays of thermal particles but also the thermal scatterings can be a dominant source as well as non-thermal production in a scenario with light sneutrinos and charged sleptons while other supersymmetric particles are heavy. We also discuss the cosmological implications of this scenario.