The father carried his son's body out of the room on his shoulders.

Literal

Father [topic-は] son's body [object-を] shouldered [then-て] room [from-から] carried-out.

かつぐ means 'to shoulder, to carry on one's back.' 運び出す is a compound verb (運ぶ + 出す) meaning 'to carry out.' An emotionally loaded sentence.