Mars likely lost a significant part of its atmosphere to space during its history. The sputtering of the atmosphere, by precipitating planetary heavy pickup ions accelerated by the solar wind, is one of the processes that could have significantly contributed to this atmospheric escape, in particular since the cessation of its global magnetic field, 4.0–4.1 Gyr ago. We present a 2 year baseline analysis of Mars Atmosphere and Volatile EvolutioN (MAVEN) observations of the precipitating flux. We use this measurement to model the expected escape rate and exospheric structure induced by this precipitation. We conclude that sputtering signatures in the dayside exosphere will be difficult to identify by MAVEN, and the induced atmospheric escape of O atoms remains orders of magnitude smaller than the expected rate induced by dissociative recombination of O2+ in Mars's ionosphere. On the contrary, deep in the nightside, Mars's sputtering might be the main source of the nonthermal part of the exospheric density profiles of species with mass larger or equal to Ar.