The badminton underarm backhand stroke is more commonly used for defensive clears and attacking clears.
The underarm stroke is fairly easy to perform compared to other badminton strokes.
This stroke is usually performed when your opponent hits a badminton drop shot to your backhand area at the front of the court.
Don't worry about generating sufficient power in this stroke. It's fairly easy to do so. In fact, worry about generating too much power while performing an underarm stroke!
If you hit an underarm clear at the front of the court too hard, the shuttle will easily land OUTSIDE the court.
Swinging Motion: You don't need to swing too hard for an underarm stroke. A gentle underarm swing is sufficient to send the shuttle right to the back of the court.
However, correct technique is still important to provide you with good body balance. The tutorial below shows you the correct way of performing a badminton underarm backhand stroke.
It's the gentle underarm swing and the gentle flick of your wrist that works together to generate the power for this stroke.
However, remember NOT to grip your racket too tightly or else your wrist action is limited.

Since you'll be hitting the shuttle IN FRONT of you, lunge forward to your backhand area. Your racket should always be in a ready position (see picture above). Your dominant leg should always be at the front when you hit an underarm stroke.

Raise your racket to the position similar to the picture above. At this point, you're preloaded and ready to perform your underarm backhand swing.

Swing upwards. Ensure that you complete your swing. This means that upon contact with the shuttle, continue with the swinging motion.
A gentle swing will do the work. You don't need to exert too much strength into your stroke or you might lose body balance.
Just before your racket makes contact with the shuttle, flick your wrist to generate the power for your underarm stroke.

The picture above shows you the position right after a completed badminton backhand underarm stroke is performed. Notice that the wrist is pointing upwards in the picture above. This means that the player have flicked her wrist during the swing.
At the same time, FOLLOW THROUGH with your swing even after you hit the shuttle (see picture above).
A backhand grip is NOT NECESSARY. However, you can switch to the backhand grip if you are fast enough to make the switch.
With a backhand grip, it'll be slightly easier to place the shuttle accurately, especially when you want to hit it across the court.
Allow the racket to FOLLOW THROUGH to enable better flight trajectory of the shuttle.