private static Image cropImage(Image img, Rectangle cropArea)
{
    Bitmap bmpImage = new Bitmap(img);
    Bitmap bmpCrop = bmpImage.Clone(cropArea,
    bmpImage.PixelFormat);
    return (Image)(bmpCrop);
}

نحوه استفاده از تابع:

private void button1_Click(object sender, EventArgs e)
{
    pictureBox2.Image = cropImage(pictureBox1.Image, new Rectangle(10,10,100,100));
}