Can you make two bedrooms into one by cutting the opening in the wall or should you build a new supporting wall?

The ability to make two adjacent bedrooms into one by knocking down a wall depends on whether the wall is load bearing. Usually, the wall between two bedrooms is not load bearing, but it is possible that it is depending on the house. If you are unsure, then either look at your home's blueprint (plan) if your local authorities have it or if you are still unsure, hire a licensed engineer to determine whether the wall is load bearing.

Even if the wall is not load bearing, it is a little more difficult to join the rooms than simply cutting a hole in the drywall. Behind the drywall there are studs which are either wood or metal. The studs need to be removed after the drywall is removed. Also there is most likely electrical wiring in the wall that needs to be removed and properly capped in the attic or crawl space. There may even be Plumbing pipes in the wall which would require moving which is a major project in and of itself. Even after removing the drywall, studs, electrical wiring, and plumbing, there will be a gap in both the ceiling and the floor that needs to be addressed. To make a long story slightly shorter, while it is possible to join two adjacent rooms, it is a lot more involved than simply cutting down the drywall.