Suspended nanowires are shown to provide mechanically controlled coherent mixing or splitting of the spin states of transmitted electrons, caused by the Rashba spin-orbit interaction. The sensitivity of the latter to mechanical bending makes the wire a tunable nanoelectromechanical weak link between reservoirs. When the reservoirs are populated with misbalanced "spin-up and spin-down" electrons, the wire becomes a source of split spin currents, which are not associated with electric charge transfer and which do not depend on temperature or driving voltages. The mechanical vibrations of the bended wires allow for additional tunability of these splitters by applying a magnetic field and varying the temperature. Clean metallic carbon nanotubes of a few microns length are good candidates for generating spin conductance of the same order as the charge conductance (divided by e2) which would have been induced by electric driving voltages.