There are many different approaches. Some people cook the filling, microwave the pepper to soften it, then add the cooked filling and then pop into the oven for 10 mins. Others, if it has a rich sauce, put it straight into the oven for 25 mins. Whatever you do, it's important to have the filling cooked, the pepper just needs to be soft, but still firm enough to hold the filling.
Here is a recipe for roast peppers stuffed with mince. In this one, rather than start in a microwave, they soften the pepper in the oven using olive oil, cook the mince separately, add it then to the softened pepper and then finish off with ten mins in the oven.
http://www.ocado.com/webshop/recipe/beef-stuffed-peppers/23566
If the beef filling is cooked, it won't be a disaster. That's the benefit of cooking the filling separately. The worst that can happen is that the pepper gets a bit burned but, if you keep an eye on it, you can take it out of the oven early. It will be soft and the mince is already cooked anyway.