We present a method to create spin-polarized beams of ballistic electrons in a two-dimensional electron system in the presence of spin-orbit interaction. Scattering of a spin-unpolarized injected beam from a lithographic barrier leads to the creation of two fully spin-polarized side beams, in addition to an unpolarized specularly reflected beam. Experimental magnetotransport data on InSb/InAlSb heterostructures demonstrate the spin-polarized reflection in a mesoscopic geometry, and confirm our theoretical predictions.