We present the discovery and characterization of two sub-Neptunes in close orbits, as well as a tentative outer planet of a similar size, orbiting TOI-1260 – a low metallicity K6 V dwarf star. Photometry from Transiting Exoplanet Survey Satellite(TESS) yields radii of R(b) = 2.33 ± 0.10 and R(c) = 2.82 ± 0.15 Rꚛ, and periods of 3.13 and 7.49 d for TOI-1260 b and TOI-1260 c, respectively. We combined the TESS data with a series of ground-based follow-up observations to characterize the planetary system. From HARPS-N high-precision radial velocities we obtain M(b) = 8.6(+1.4,−1.5) and M(c) = 11.8(+3.4,−3.2) Mꚛ. The star is moderately active with a complex activity pattern, which necessitated the use of Gaussian process regression for both the light-curve detrending and the radial velocity modelling, in the latter case guided by suitable activity indicators. We successfully disentangle the stellar-induced signal from the planetary signals, underlining the importance and usefulness of the Gaussian process approach. We test the system’s stability against atmospheric photoevaporation and find that the TOI-1260 planets are classic examples of the structure and composition ambiguity typical for the 2–3 Rꚛ range.