。
Mother bandaged Jim's cut.
Literal
Mother [topic-は] Jim [gen-の] cut [on-に] bandage [obj-を] did.
包帯をする is a noun + する construction that functions as a single verb meaning 'to bandage' — Japanese often prefers this pattern to a dedicated verb. The particle に marks the destination of the bandage (where it was applied), not a direction of motion. 切り傷 is a compound of 切る and 傷 ('cut-wound') — a productive pattern for specifying types of injuries.