FOLLOW UP - Might Mug has made good on the problem. I called back the next day (more about the fact that I was left on hold while everyone left for the day than getting a new mug - that really had me upset). When I called back, the customer service person I spoke with listened to what happened the previous day and apologized for the poor service. Then she went on to say that because of the poor service experience, she would replace my broken mug and all I had to do was send her pictures of the broken mug to show what was wrong. She told me this was to identify that the mug is really theirs and not a knock-off which they apparently have had.
I am glad this customer service person was so much better than the person who left me on hold the previous day.