I think you must first duplicate (or duplicate linked), then use NKEY to get the numerical palette and type in a minus in front of the size of the axis you want it to mirror around (I think), and type enter. For ex. size X: -1.000. You need to experiment to get it right.
(being sure to have the curser at the point you want to mirror around and that you’ve selected the cursor to be the rotation point, ie: hit the ‘.’ period key over the 3D window that you’re using.