On the other hand, it helped that doosmday, exceptionally, can make superman bleed with its sharp extremities. Not being an anime character, supes cannot afford to lose multiple gallons of blood. Jack, on the other hand, is an anime character so doosmday cannot kill him with blood loss!
but repeatet blunt trauma from someone with superman+ levels of strength can penetrate even his abnormaly thick skull, and knock him unconcious.