Is sepsis contagious?

Not exactly: Sepsis is not a disease in and of itself - it is a syndrome (a constellation of symptoms) that result from the bodies attempt to fight off a severe infection +/- any direct toxins from the bacterium itself. The causes of sepsis can be contagious or not (for example, a urinary tract infection is not directly contagious, but pneumonia often is).

Not usually: Sepsis is defined as systemic inflammatory response syndrome, sirs (2 or more of fever, rapid pulse, rapid breathing, elevated white blood cell count) caused by an infection. Most cases of sepsis are not contagious but if the infection causing the sepsis is contagious than that infection could be spread.