The torsional dynamics of a semiflexible polymer with a contour length L larger than its persistence length L_p that is rotated at fixed frequency ω₀ at one end is studied by scaling arguments and hydrodynamic simulations. We find a non-equilibrium transition at a critical frequency ω_*: In the linear regime, ω₀<ω_*, axial spinning is the dominant dissipation mode. In the non-linear regime, ω₀>ω_*, the twist dissipation mode involves the continuous creation of plectonemes close to the driven end and the rotational friction is substantially reduced.