Imam Al-Mahdi (AS) will remove injustice and tyranny from the whole world. His time of re appearance will be filled with injustice and tyranny. That does not means by any mean that we have to add on injustice and wrong to hasten his re appearance, but on the contrary, we remain as sincere followers of Ahlul Bayt (AS) responsible to do and spread good deeds which is the aim of our Infallible Imams and all the prophets (AS).
The bad deeds are from bad people as Allah (SWT) says in Quran: Evil deeds has appeared on land and sea because of what people have committed. Al-Room: Verse 41.
We should always prevent and counter evil deeds by doing and spreading good deeds but our efforts will never be enough, and the injustice and tyranny will go on till the re appearance of The Divine Leader from Allah who will remove away the evil and establish the pan state of Good and Justice.
There is no dichotomy at all.