We study the non-equilibrium regime of a mechanical resonator at low temperature realized with a suspended carbon nanotube quantum dot contacted to two ferromagnets. Due to spin- orbit interaction and/or an external magnetic gradient, the spin on the dot couples directly to the flexural eigenmodes. Owing to this interaction, the nanomechanical motion induces spin-flips of the electrons passing through the nanotube. When a finite voltage is applied, a spin-polarized current causes either heating or active cooling of the mechanical modes, depending on the gate voltage. Optimal cooling is achieved at resonance transport realized when the energy splitting between two dot levels of opposite spin equals the resonator frequency. We show that weak interaction coupling strength and moderate polarization can achieve ground state cooling.