I was startled by the severity of my mother's anger.

Literal

Mother [possessive-の] anger [possessive-の] severity [to-に] was-startled

怒りの厳しさ — ~さ turns 厳しい (severe) into the abstract noun 厳しさ (severity). Multiple の chain: 母親の怒りの厳しさ. に marks the cause of surprise. Subject omitted.