Clip subviews content out of bounds
In iOS when you want to clip part of the subviews that are out of the bounds you just set clipsToBounds = YES; in the parent view.
In Android you set setClipChildren(true); in the ViewGroup.
React Native tries to mimic CSS with their own implementation of it, so you can set the property overflow: 'hidden' in the view's style.
Easy as pie!