When we prepare our purple onions for cooking we always break the segments by hand to appreciate their texture and know what to discard and what to keep (in case there is any rot). The thinnest segments can sometimes be bitter tasting, and if an outer segment has some beginnings of rot breaking the segments by hand will let you separate it out from the good onion parts. 
Some Purple Onion Segments
Your purple onion segments should snap easily in your fingers as you break them up. We usually make ours to be about 1 inch or so square. The best purple onions (being so squat) are typically about 1 inch or a bit more tall, and we break the segments at one inch intervals to make pieces about 1 inch square overall.