Use the Bitmap.Clone method:
Bitmap bm = new Bitmap( @"D:\Temp\MyPic.jpg" );
int w = bm.Width / 2;
int h = bm.Height / 3;
Rectangle rTL = new Rectangle( 0, 0, w, h );
Rectangle rBR = new Rectangle( w, h, w, h );
Bitmap bmTL = (Bitmap)bm.Clone( rTL, bm.PixelFormat );
Bitmap bmBR = (Bitmap)bm.Clone( rBR, bm.PixelFormat );