。
She gets upset over the smallest things.
Literal
She [topic-は] trivial things [over-で] right-away mood [object-を] [hurts-害する].
気分を害する ('to be upset, take offense, hurt one's feelings') is a slightly formal idiom — literally 'damage one's mood.' Common in apologetic register: お気分を害されたなら申し訳ありません ('I apologize if I've caused offense'). つまらない ('trivial, dull, worthless') here describes the cause, not a person's character. The で marks the cause/trigger of the emotional reaction — つまらない事で ('over trivial things'). すぐ ('right away, easily') paints habitual quickness rather than rare reaction. Together: a portrait of someone with a short fuse for small slights.