I'm angry about your groundless accusations.

Literal

I [topic-は] you [possessive-の] basis-lacking [attributive-の] criticism [to-に] stomach [subject-が] is-standing [explanatory-んだ].

腹が立つ (はらがたつ, 'to get angry') is an idiom — literally 'the stomach stands up.' 根拠のない ('groundless, baseless') — 根拠 ('basis, grounds') + のない. 非難 (ひなん, 'criticism, blame, accusation'). んだ adds explanatory emphasis to the anger.