Fetching details from the dictionary...

to wound; to injure
to hurt someone's feelings (pride, etc.)
to damage; to chip; to scratch
何気ない一言が相手の心を傷つけることがある。
A casual remark can sometimes wound another person's feelings.
家具を運ぶ際に壁を傷つけないように注意した。
I was careful not to damage the walls while moving the furniture.
彼の言葉が心を傷つけた。
His words hurt me deeply.