She expressed her gratitude to everyone who had supported her.

Literal

She [topic-は] self [object-を] supported [for her-てくれた] people all [to-に] gratitude [of-の] feeling [object-を] expressed.

自分を支えてくれた人みんな (everyone who supported her) is a relative clause with てくれた marking the support as a favor received. 感謝の意を表す (to express gratitude) is a formal set phrase: 感謝 (gratitude) + 意 (feeling/intention) + を表す (to express). The combination of colloquial みんな (everyone) with formal 感謝の意を表す creates a natural register blend for a thank-you speech.