Is there a way to get the missions to reset faster?

I'm assuming there isn't but I figured I'd ask.

Other than not writing a good forum post (short topic, longer body), do you play the game much?   You seem to ask very basic questions about the game.   

That said, many ways to reset missions but I am assuming you don't want to pay diamonds for the reset of an area or the whole map.

Then the next best thing to do is to do a short mission (usually a fight mission) in that area to reset that zone.   Otherwise you need to level up for a full reset.

Those indeed are the simple ways to reset areas. 

To expand: you can reset the missions in just 1 area or the whole field.

Also sometimes there is an event, that gives reset missions, but those are announced.