No, there isn’t actually an option that allows you to restart a mission or level in Valkyria Chronicles. You’ll only get that option once you lose the battle and get a Game Over screen. However, there are a couple of in-game things you can do to quickly attempt a mission again from the beginning.
Make a save file – The first thing you should do right at the start of any battle is save your game. Simply head into the options menu once the briefing is over, and create a new save file. That way, if you ever need a quick restart in the middle of battle, you can bring up your options menu again, and load your save file from there. It’s not perfect, but it’s a lot faster than quitting the game entirely and booting it up again.
Blow up the Edelweiss – This isn’t the most elegant solution, but it will get the job done. If you screwed up a turn and you want to restart, but forgot to create a separate save file, you can destroy the Edelweiss to get a quick Game Over screen. If you have a lancer and 1 CP left, simply get the lancer to fire a rocket at the weak spot found on the back of the Edelweiss. This will kill Welkin, and cause you to fail the mission automatically. You will then get the option to restart the mission.
As a side note, it’s also a good idea to save your game in the middle of the battle. If you’re about to take a risky shot, save your game before attempting it. If your gamble doesn’t pan out, you can always reload that last save quickly and try again.