This paper presents a spatially-resolved kinematic study of the jellyfish galaxy JO201, one of the most spectacular cases of ram-pressure stripping (RPS) in the GASP (GAs Stripping Phenomena in Galaxies with MUSE) survey. By studying the environment of JO201, we find that it is moving through the dense intra-cluster medium of Abell 85 at supersonic speeds along our line of sight, and that it is likely accompanied by a small group of galaxies. Given the density of the intra-cluster medium and the galaxys mass, projected position and velocity within the cluster, we estimate that JO201 must so far have lost ~50% of its gas during infall via RPS. The MUSE data indeed reveal a smooth stellar disk, accompanied by large projected tails of ionised (Halpha) gas, composed of kinematically cold (velocity dispersion <40km/s) star-forming knots and very warm (>100km/s) diffuse emission which extend out to at least ~50 kpc from the galaxy centre. The ionised Halpha-emitting gas in the disk rotates with the stars out to ~6 kpc but in the disk outskirts becomes increasingly redshifted with respect to the (undisturbed) stellar disk. The observed disturbances are consistent with the presence of gas trailing behind the stellar component, resulting from intense face-on RPS happening along the line of sight. Our kinematic analysis is consistent with the estimated fraction of lost gas, and reveals that stripping of the disk happens outside-in, causing shock heating and gas compression in the stripped tails.