The consequences of erosion caused by the mutual interaction of water droplets with sedimentary rock such as sandstone are not satisfactorily elucidated in the literature. This topic is important from many points of view, and its practical applications include the protection of cultural heritage or the targeted removal of material. This study assessed the wear rates on Božanov sandstone caused by multiple-droplet impingement, with water droplet impact speeds of v = 58 m/s, 92 m/s and 127 m/s corresponding to supply pressure of p = 2, 5 and 10 MPa, respectively. As a droplet generator, a pulsating water jet with a frequency of 20 kHz was used. Water droplets determined by a nozzle diameter d = 1 mm were distributed along a linear trajectory three times for each run. The water droplet impact density was varied by changing the traverse speed. In order to investigate the development of integrity damage, the samples were scanned using a digital microscope. Material loss was determined via weighing and compared using a non-contact measuring method. The results showed that the erosion responses, such as erosion depth and volume removed, increased with an increase in the supply pressure and a decrease in traverse speed. Moreover, it was found that at the lowest supply pressure p = 2 MPa, the effect of the number of drops density is invariant for traverse speeds in the range of 1–10 mm/s. When the pressure was increased from 5 to 10 MPa, the material removal values tripled. This significant increase may be attributed to the formation of an abrasive pulsating water stream within the created groove.