No, it is not part of the Mormon religion. Just asked my husband- he was raised Mormon. But, this is something my husband, and hipsters, and lumberjacks alike engage in.
Admittedly, up until now, I thought the word was pogontomy. Please ignore our misspell on the video. We are all learning here! Now consider yourself schooled and go find some bearded man to ask if he is into pogonotomy. And don’t forget to watch the video!