With the approach of the close encounter of comet Siding Spring with Mars, possible influences on the Martian atmosphere from the cometary coma are being explored. Here we describe the non-thermal atmospheric loss due to atmospheric sputtering produced by the impact of the coma material. We use an atmospheric sputtering model to simulate the effect of the incident neutral O and the pickup O+, produced by photodissociation of water and its products. With the relatively large encounter speed of 56 km/s at a close flyby altitude of ~130,000 km, the sputtering escape rates from the coma can reach 2-3 times the incident gas fluxes. Thus, the passing of the cometary coma will lead to removal of Martian atmosphere instead of mass loading. If the cometary outgassing rate reaches 1028s-1, the sputtering from the extended coma could remove about 10 tons of Martian gases and deposit about 1 ton of external cometary material into the atmosphere during the one hour encounter. This implies that the cometary sputtering may have played a non-negligible role in Mars atmospheric evolution when this kind of cometary encounter may occur frequently in early Martian epochs.