On Food Network Cake Challenges, I often see them cut a hole in the center of several cakes and "thread" them down over a center PVC-type support. When that's done, how do you go about cutting the cakes? Do you leave them on the center support and just cut around it, or do you have to remove them for cutting?

With those special creations inner support you speak of is a must.
Yes, you do leave that type of support in the cake or it would fall
They would just have to cut aorund it.

I've never cut a cake that qualified as a FN Challenge cake, but I have cut some cakes (made by other bakeries) that had a center support of some sort. I either pull the support out of the cake or lift the tiers up off of the center support.

What about the multiple smaller support dowels, what's the secret to cutting around those or pulling them out without making a mess?

For the smaller doweled cakes I just pull the dowels out and then slice. For the centeral supports I too would just pull the tier up and off and then slice that way the rest of the cake still has it's support in it if it's not going to be used straight away.

I would imagine having to cut round dowels would be a PIA!

Usually I have to end up cutting around the center support, because there isn't a way to lift off the tiers without ripping apart the cake....like my zombie cake. I actually have a pic of the zombie cake after they started cutting it. You can see how the center support sticks out. There's a cake board mid body to help with cutting and stability.