Edit gif

[rich2005]

Unfortunately, you can not do that for an animation. You need some way of applying the mask to all layers in the group, then devolve the layer group into layers outside the group for the animation.

Do you know of a simple way ?

It is the transparency shown by the OP screenshot which is a problem. Several ways of blanking out part of each layer, the Saule Goode script, Ofnuts has a clear-layers.py plugin which applies the BG colour to a selection in all layers. Bound to be others, but so far I have not seen a cut-selection on all layers script.

Edit: Ofnuts clear-layers.py plugin does work. That example animation did not have alpha on all layers. Another plugin such as multiple-layer-actions required  Looks like it will be the easiest way.  http://sourceforge.net/projects/gimp-too...s/scripts/    near the bottom of the list clear-layers-0.2.py dated 2012-03-12
There is a alpha-to-all-layers script here: http://gimpchat.com/viewtopic.php?f=9&t=1718#p21494

Ah... It is an ancient script but it does all that is required. Add alpha to all layers then cut a selection. I like scripts for very occasional use, I can load them without restarting Gimp.  Mupltiple-Layer_Actions.scm zipped and attached

Works like this 30 second demo: https://i.imgur.com/vda1Oa5.mp4