To create a copy of the crop we want, we can do the following,
// Read img
cv::Mat img = cv::imread("imgFileName");
cv::Mat croppedImg;
// This line picks out the rectangle from the image
// and copies to a new Mat
img(cv::Rect(xMin,yMin,xMax-xMin,yMax-yMin)).copyTo(croppedImg);
// Display diff
cv::imshow( "Original Image", img );
cv::imshow( "Cropped Image", croppedImg);
cv::waitKey();