We present photometric and spectroscopic observations of the low-mass X-ray binary GR Mus (XB 1254-690), and find strong evidence for the presence of a negative superhump with a period that is 2.4 ± 0.3 per cent shorter than the orbital. This provides further support that GR Mus indeed harbours a precessing accretion disc (with a period of 6.74 ± 0.07 d) that has retrograde precession and is completely tilted out of the orbital plane along its line of nodes. This tilt causes a large fraction of the gas in the accretion stream to either over- or underflow the accretion disc instead of hitting the disc rim, and could be a feature of all low-mass X-ray binaries with characteristics similar to GR Mus (i.e. the so-called atoll sources). Furthermore, we also find marginal evidence for the presence of a positive superhump, suggesting that the accretion disc in GR Mus is eccentric due to tidal resonances. If true, then the relationship between the positive superhump period excess and the mass ratio (q) provides a constraint of q = Mdonor/MNS = 0.33-0.36. Together with the radial velocity semi-amplitude measurements of the compact object, and previous modelling of the inclination we obtain a mass for the neutron star of 1.2 ≤ MNS/M⊙ ≤ 1.8 (95 per cent confidence).