Polarizing electron beams using light is highly desirable but exceedingly challenging, as the approaches proposed in previous studies using free-space light usually require enormous laser intensities. Here, we propose the use of a transverse electric optical near field, extended on nanostructures, to efficiently polarize an adjacent electron beam by exploiting the strong inelastic electron scattering in phase-matched optical near fields. Intriguingly, the two spin components of an unpolarized incident electron beam-parallel and antiparallel to the electric field-are spin-flipped and inelastically scattered to different energy states, providing an analog of the Stern-Gerlach experiment in the energy dimension. Our calculations show that when a dramatically reduced laser intensity of ∼10^{12} W/cm^{2} and a short interaction length of 16 μm are used, an unpolarized incident electron beam interacting with the excited optical near field can produce two spin-polarized electron beams, both exhibiting near unity spin purity and a 6% brightness relative to the input beam. Our findings are important for optical control of free-electron spins, preparation of spin-polarized electron beams, and applications in material science and high-energy physics.