I bought the Stanley 20-800 Contractor Grade Clamping Mitre Box to cut 4" diameter mailing tubes. It works great. It pushes the limit for height on but does fit. This seems so much safer than using a utility knife or power tool.
I follow up the cut with a couple of quick pulls of a fine sanding block and pop a cap on one side for quick loading of the tube and so I don't have to store as many caps. Initially, I ordered 24" tubes from ULine.com, but the 36" tubes were cheaper so by cutting down a 36", I can get a 24" tube, a 12" tube and extra caps for less than a 24" tube.
I purchased mailing tubes and extra caps from ULine and the saw from Amazon.com.