In a fit of anger, he said whatever he pleased and then left.
Literal
Anger-driven [target-に] he [topic-は] say-as-one-pleases things [object-を] said-and, returned went.
腹立ちまぎれに means 'in a burst of anger' — まぎれ means 'in the confusion/heat of.' 言いたい放題 means 'saying whatever one wants' — 放題 means 'as much as one likes.' 帰って行った chains departure.