Holding your breath is common, standard, well-accepted powerlifting practice. Hold your breath throughout each rep of squatting, deadlifting, and pressing.
Holding your breath helps keep your chest locked. Breathing during the rep encourages you to move your chest, meaning you lose the tightness in your abs, upper and lower back. This invites injury. For instance, I was blasting through a good set of deadlifts, but pulled a muscle in my back when I let myself breath out on the way up.
If you feel like you need to let your breath out in the middle of a rep, sometimes you have to dump the bar and lose the rep. (Other times you can grind it out.)
The Mayo Clinic is wrong. I assume, since they do not give reasons or evidence for their claim that holding one's breath is dangerous, that they think that holding one's breath while lifting could cause some sort of stroke or aneurysm. See pages 50-54 in Starting Strength 2nd edition for a discussion of why this is incorrect, where, among other things, it is noted that
There are no data for the rates of CVA [cerebrovascular accidents] in the weight room, because they occur so infrequently as to be statistically unmeasurable.
The Mayo Clinic is speaking to a broad audience, and so gives watered-down lifting advice. Since they're working with people who are decrepit, disabled, detrained, and have no in-person coaching, it makes sense for them to recommend lifting light weights for high reps while breathing. It's just not good advice for anyone who's engaging in actual training, instead of exercise-cum-physical-therapy.