How to cut out areas from a layout consists of different objects

You are on track if you built each body part on separate layers and named them.

The only issue is the pose.  If you watch the tutorials for Adobe Character Animator you will see the arms are use slightly out to the side and the legs spread a little more.  I also feel there should be more space betwen the legs, as you will run into some overlaps.

I always place my slightly out and legs slightly spread apart when creating characters for Adobe Character Animator or Animate... or even After Effects.

I would also go the Clipping Mask route. As you animate, you might find that you need a little more of the clothing and if you cut ot off, it will be gone, whereas if you use this method, you will have the ability to make adjustments if need be.

You can use Pathfinder >> Minus Front

Select the body part, and a copy of the area you want to remove. 

If you already have the clothes made, I'd suggest duplicating the body parts to the clothes layers. For each part, use a dupe of the clothes, and create a clipping mask with the body part paths (https://helpx.adobe.com/illustrator/using/clipping-masks.html)
To manage these so they transform together during animation, you may have to rearrange your layers afterwards, so that the clothes are just above the body parts. That way, you can easily select them both for each transformation.