'Ease the burden' would be a more natural choice. Another phrase with a similar meaning is 'lighten the load'. 'Mitigate' is a very formal word, typically used in phrases like 'mitigate the damages' (in a legal context), or 'mitigate the adverse side effects' (in a medical context).

Relieve the burden I would only use mitigate in formal office communication, or an academic environment. Most people haven't the foggiest clue what it means.