We put theoretical constraints on the presence and survival of icy grains in debris discs. Particular attention is paid to UV sputtering of water ice, which has so far not been studied in detail in this context. We present a photosputtering model based on available experimental and theoretical studies. We quantitatively estimate the erosion rate of icy and ice-silicate grains, under the influence of both sublimation and photosputtering, as a function of grain size, composition and distance from the star. The effect of erosion on the grains location is investigated through numerical simulations coupling the grain size to its dynamical evolution. Our model predicts that photodesorption efficiently destroy ice in optically thin discs, even far beyond the sublimation snow line. For the reference case of beta Pictoris, we find that only > 5mm grains can keep their icy component for the age of the system in the 50-150AU region. When taking into account the collisional reprocessing of grains, we show that the water ice survival on grains improves (grains down to ~ 20 um might be partially icy). However, estimates of the amount of gas photosputtering would produce on such a hypothetical population of big icy grains lead to values for the OI column density that strongly exceed observational constraints for beta Pic, thus ruling out the presence of a significant amount of icy grains in this system. Erosion rates and icy grains survival timescales are also given for a set of 11 other debris disc systems. We show that, with the possible exception of M stars, photosputtering cannot be neglected in calculations of icy grain lifetimes.
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