It is widely accepted that Titan and the mid-sized regular satellites around Saturn were formed in the circum-Saturn disk. Thus, if these mid-sized satellites were simply accreted by collisions of similar ice-rock satellitesimals in the disk, the observed wide diversity in density (i.e., the rock fraction) of the Saturnian mid-sized satellites is enigmatic. A recent circumplanetary disk model suggests satellite growth in an actively supplied circumplanetary disk, in which Titan-sized satellites migrate inward by interaction with the gas and are eventually lost to the gas planet. Here we report numerical simulations of giant impacts between Titan-sized migrating satellites and smaller satellites in the inner region of the Saturnian disk. Our results suggest that in a giant impact with impact velocity > 1.4 times the escape velocity and impact angle of ~45 degree, a smaller satellite is destroyed, forming multiple mid-sized satellites with a very wide diversity in satellite density (the rock fraction = 0-92 wt%). Our results of the relationship between the mass and rock fraction of the satellites resulting from giant impacts reproduce the observations of the Saturnian mid-sized satellites. Giant impacts also lead to internal melting of the formed mid-sized satellites, which would initiate strong tidal dissipation and geological activity, such as those observed on Enceladus today and Tethys in the past. Our findings also imply that giant impacts might have affected the fundamental physical property of the Saturnian mid-sized satellites as well as those of the terrestrial planets in the solar system and beyond.