How can I 'cut' a transparent hole in a UIImage?

Just needed the Version from @Fattie, thanks again! Here is the updated Code for Swift 5.1:

private func cut(holeRect: CGRect, inView view: UIView) {
    let combinedPath = CGMutablePath()
    combinedPath.addRect(view.bounds)
    combinedPath.addRect(holeRect)

    let maskShape = CAShapeLayer()
    maskShape.path = combinedPath
    maskShape.fillRule = .evenOdd

    view.layer.mask = maskShape
}

If you want the cutout to have rounded corners you can replace combinedPath.addRect(holeRect) with rectanglePath.addRoundedRect(in: holeRect, cornerWidth: 8, cornerHeight: 8).

Presume that your image is being displayed in a view - probably a UIImageView. Then we can punch a rectangular hole in that view by masking the view's layer. Every view has a layer. We will apply to this view's layer a mask which is itself a layer containing an image, which we will generate in code. The image will be black except for a clear rectangle somewhere in the middle. That clear rectangle will cause the hole in the image view.

So, let self.iv be this UIImageView. Try running this code:

CGRect r = self.iv.bounds;
CGRect r2 = CGRectMake(20,20,40,40); // adjust this as desired!
UIGraphicsBeginImageContextWithOptions(r.size, NO, 0);
CGContextRef c = UIGraphicsGetCurrentContext();
CGContextAddRect(c, r2);
CGContextAddRect(c, r);
CGContextEOClip(c);
CGContextSetFillColorWithColor(c, [UIColor blackColor].CGColor);
CGContextFillRect(c, r);
UIImage* maskim = UIGraphicsGetImageFromCurrentImageContext();
UIGraphicsEndImageContext();
CALayer* mask = [CALayer layer];
mask.frame = r;
mask.contents = (id)maskim.CGImage;
self.iv.layer.mask = mask;

For example, in this image, the white square is not a superimposed square, it is a hole, showing the white of the window background behind it:

EDIT: I feel obligated, since I mentioned it in a comment, to show how to do the same thing with a CAShapeLayer. The result is exactly the same:

CGRect r = self.iv.bounds;
CGRect r2 = CGRectMake(20,20,40,40); // adjust this as desired!
CAShapeLayer* lay = [CAShapeLayer layer];
CGMutablePathRef path = CGPathCreateMutable();
CGPathAddRect(path, nil, r2);
CGPathAddRect(path, nil, r);
lay.path = path;
CGPathRelease(path);
lay.fillRule = kCAFillRuleEvenOdd;
self.iv.layer.mask = lay;

Here's a simple Swift function cut#hole#inView to copy and paste for 2017

func cut(hole: CGRect, inView view: UIView) {
    let path: CGMutablePath = CGMutablePath()
    path.addRect(view.bounds)
    path.addRect(hole)

    let shapeLayer = CAShapeLayer()
    shapeLayer.path = path
    shapeLayer.fillRule = .evenOdd

    view.layer.mask = shapeLayer
}